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."
20. April 2018
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|Klopp: Bayern Munich move would´ve been complicated|
|Mask-wearing Joel Embiid cleared to face Heat|
|Wenger names Vieira as potential Arsenal successor|
|Simeone demands more alert Atletico to solve away day problems|
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|Sixers´ Embiid upgraded to probable for game three against Heat|
|Malaga relegated from LaLiga after late defeat|
|Conte reaches 100 Chelsea games with win at Burnley|
19. April 2018
|When I fail, I get really angry - Morata apologises for tantrum|
|Neymar names players to watch at World Cup|
|Hughes remains upbeat despite Leicester draw|
|Hull inflict more drop-goal misery on Leeds|
|Two strikers an FA Cup option for Conte´s Chelsea|
|I´m not finished, Chelsea captain Cahill insists|
|I´m going to get there - Djokovic confident of rediscovering best form|
|Pedrosa cleared to race in Austin after wrist surgery|
|Leicester City 0 Southampton 0: Saints´ survival bid suffers fresh blow|
|Burnley 1 Chelsea 2: Conte´s men boost top-four chances with FA Cup warm-up|
|Fenerbahce-Besiktas abandoned after Gunes struck by object thrown from crowd|
|Quiros´ birdie-birdie finish earns a share of Rabat lead|
|New York Giants release Brandon Marshall|
|Real Sociedad 3 Atletico Madrid 0: Barca´s title party set to start|
|Thiem ready to up level for ´ultimate challenge´ of Nadal|
|Carrick reveals depression led to England exile|
|´Who are they?!´ - Accrington milk promotion with supermarket stunt|
|Mouthwatering Nadal-Djokovic quarter-final scuppered by Thiem|
|Stunning Gayle century ends Sunrisers´ unbeaten start|
|Conte names Hazard on bench for Burnley clash|
|Rooney denies rift with Everton boss Allardyce|
|Kane will leave Tottenham unless they win trophies, predicts Souness|
|Porzingis could miss 2018-19 season, Knicks owner says|
|Portugal´s Sanches has no chance of World Cup selection - Carvalhal|
|Spurs coach Popovich to miss game three after death of wife|
|Nadal reaches 14th straight Monte Carlo quarter-final|
|Better with one arm - Julio Cesar reveals Mourinho´s Casillas jibe|
|New Hamilton deal ´agreed in principle´ for Mercedes|
|Joseph likely to miss England´s tour of South Africa|
|Mourinho has nothing to prove - Pochettino|
|Bhatti pens one-year Glasgow extension|
|I have spoken to the chairman - Allardyce upset by Everton survey|
|Kit cat: Bath player offers signed shirt for missing pet|
|Emery dismisses talk of Real Sociedad offer|
|Thiem rallies to send Djokovic packing in Monte Carlo|
|Sidibe´s Monaco season over but World Cup return possible|
|Guardiola thanks ´unique´ City staff in celebration speech|
|Wan-Bissaka signs long-term Crystal Palace extension|
|Love will be ready for game three, assures Cavs coach Lue|
|Injured Raonic withdraws from Monte Carlo, Cilic advances|
|ECB announces 100-ball format for new domestic competition|
|Bottas aiming to overthrow Hamilton and claim world title|
|Rakitic to make comeback following finger surgery|
|FIFA dismisses Brewster racism complaint from U-17 World Cup final|
|Isak could benefit from Batshuayi injury - Stoger|
|Mitchell on target again in scrappy Roosters win|
|Shaw hopes to have earned FA Cup start|
|Mercado: If I smack Messi, I can´t go back to Argentina!|
|Salah wants Golden Boot to prove Chelsea doubters wrong|
|Chelsea´s Alonso gets three-game ban for Long challenge|
|Atletico clash absolutely vital to Arsenal´s season, admits Wenger|