Arsenal have not issued a contract ultimatum to Mesut Ozil or Alexis Sanchez.
Talk over the future of the two attacking stars, whose deals run out at the end of this season, has dominated the agenda at Emirates Stadium for months.
Speaking ahead of Wednesday's Premier League trip to West Ham, Wenger responded to reports Ozil has been given a bumper final offer of £275,000 per week by confirming talks are ongoing with both players.
"The conversations are, as always, going on with everybody. Our door is always open. I cannot tell you much more," said the Arsenal boss.
"I have said many times we want to keep them and, at the moment, that's all we can say. The best way to deal with these kind of things is to keep it as discreet as possible."
Asked whether a "take-it-or-leave-it" offer had been made, Wenger replied: "No."
Another Arsenal player whose future is seemingly up in the air as the transfer window approaches is Olivier Giroud.
The France striker equalled ex-Manchester United favourite Ole Gunnar Solskjaer at the weekend, his 17th goal as a Premier League substitute to snatch a point at Southampton the level best for a single club.
But Giroud, who was linked to Everton before the start of the campaign, has made all 13 of his top-flight appearances from the bench since Alexandre Lacazette's arrival from Lyon.
"He is not a super-sub for me, he is a regular player. I have plenty of good strikers and I cannot play all of them together," said Wenger, who is not keen on a January sale.
"I speak to all my players but it is very difficult to speak about what we talk about.
"He is a very important player. I have big respect for him and I am an admirer of Olivier Giroud. Look at how many French caps he has got since he joined Arsenal. I do not think he has wasted his time.
"Personally, I want him to stay at the club until the end of the season and then we'll see.
"I can give you 10 more cases. Every player who doesn't play wants to start in the Premier League."
19. Oktober 2018
|Vile and abhorrent – Chelsea´s Carney responds to online abuse|
|Giants WR Beckham Jr. explains why he might cramp up: ´I really don´t like water´|
|Man City pay training-pitch tribute to Joe Hart|
|Neymar to be rested as Tuchel rubbishes Ballon d´Or concerns|
|Sarri ´not interested´ in Christensen father´s quit threat|
|Cardinals fire offensive coordinator McCoy after 1-6 start|
|Neymar return unlikely, but anything can happen – Valverde|
|Bairstow a doubt for fourth ODI|
|Manchester United fined for late arrival and delayed kick-off against Valencia|
|Australia-Pakistan chat not ´especially polite´ - Sarfraz|
|Pogba relishing ´pressure game´ against in-form Hazard|
|Don´t bet on Cardiff survival, warns Warnock|
|Buffon enjoying Tuchel´s methods at PSG|
|RIP to Wimbledon epics! Isner feels like The Undertaker following final-set tie-break rule|
|Sevilla performance sealed Bernat´s Bayern exit - Hoeness|
|Keita set to miss out as Liverpool monitor injured stars|
|He didn´t want to be here – Guardiola doubts Sancho will return to Manchester City|
|Sarri: Manchester United are the best in the Premier League|
|Mourinho salutes ´brave´ Shaw for ´best possible´ response to criticism|
|No Ballon d´Or distractions for Griezmann, insists Simeone|
|Wigan stand by Hardaker as full-back prepares to undergo rehabilitation|
|Barcelona deny Neymar talk|
|Hazard can win the Ballon d´Or as a Chelsea player, insists Sarri|
|De Bruyne in contention to start in Manchester City´s clash with Burnley|
|Neymar needs to mature to reach Messi levels - Xavi|
|We have a hell of a lot to do - Paine slams Australia batting|
|Kerber and Osaka to meet at WTA Finals|
|Lorenzo out of Japanese MotoGP|
|Real Madrid handed Africa trip in Copa del Rey|
|Allegri: Ronaldo has sharpened Juventus focus|
|No Wade in Wasps squad amid NFL reports|
|Rooney: Five of us controlled Man United dressing room|
|Bayern bosses launch scathing attack on ´disrespectful´ media|
|Saints lock in Lawes to new deal|
|Adelaide United 1 Sydney 1: Debutant Le Fondre rescues a point|
|Madrid can´t look back, only forward - Lopetegui confident of revival|
|Wimbledon to introduce final-set tie-breaks|
|Abbas inspires Pakistan to series victory|
|Madrid boss Lopetegui hopeful on Bale availability|
|Mood is positive at Bayern, insists under-pressure Kovac|
|LeBron offers food for thought after losing Lakers debut|
|Bolt future not an immediate concern for Mariners|
|Hazard: I could finish my career at Chelsea|
|Buffon hoping to avoid Champions League final against Juventus|
|Wilshere not ready for West Ham return|
|Chelsea v Manchester United: Hazard better under Sarri than he ever was with Mourinho|
|The big Friday Premier League quiz|
|Khawaja suffers meniscal tear, doubt for India series|
|Babbel: Klopp must win trophies now at Liverpool|
|LeBron makes spectacular start on Lakers debut, but LA fall to Trail Blazers|
|Broncos thrash Cardinals to end losing streak|
|Price leads Red Sox past Astros and into World Series|
|LeBron makes fast start on Lakers debut with two massive dunks|
|Real Salt Lake 4 New England Revolution 1: Hosts boost play-off chances|
|Simmons gets triple-double in win over Bulls|
|´Ambitious´ Maguire wants Champions League football|
|Henry praises ´charismatic leader´ Falcao|
|WATCH: Cardinals WR Fitzgerald tackles former QB Warner on sidelines|
|Spurs right not to make signings – Pochettino|
|Icardi happy at Inter, close to contract renewal|
|This Week in U.S. Sports: Bosa leaves Ohio State while the World Series is almost set|
|Liverpool boost as Salah and Van Dijk join training|
|Cowboys discuss road woes, Prescott says team ´addressed the elephant in the room´|
|Isner scrapes through in Stockholm, Monfils eliminates Tsonga|
18. Oktober 2018
|Hinch says Altuve would be out with injury in regular season|
|WATCH: Schwarzenegger tells LeBron to make Lakers great again|
|LeBron tells Lakers coach Walton: I´m always fresh!|
|Mayweather should come back to fight me - Alvarez|
|Goerges battles past Vekic, Kasatkina wins all-Russian tie|
|Ask 32,000 Gibraltarians if the Nations League is meaningless - Styche|