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."
|Durant continues dominance over Cavs as Warriors win|
|Halep survives scare and rolled ankle at Melbourne Park|
|Westbrook ejected against Kings after arguing call|
|Djokovic eases past Young on return|
|Sharapova staying grounded after Melbourne win|
|Neville: Mourinho would happily swap Mkhitaryan for Sanchez|
|Raonic suffers surprise loss in Melbourne|
|Sharapova wins on return to Australian Open|
|Pirates send McCutchen to Giants|
|Man United becoming Pogba´s team – Mourinho|
|Saints, Steelers coaching staffs to lead Pro Bowl teams|
|LeBron says we cannot let racism ´conquer us as people´|
|Super Bowl hopeful Belichick cautiously preparing for Jaguars|
|Cardinals veteran Yadier Molina: Three more years before retirement|
|The best finishes in NFL playoff history - Where does Keenum & Diggs´ Minneapolis miracle rank?|
|Can ´talking with everyone´ but hints at Liverpool stay|
|Mourinho ´not unconfident´ Manchester United will sign Sanchez|
|Pogba warns City that United will not give up the chase|
|Assist king Pogba matches De Bruyne, Sane despite injury and suspension|
|Manchester United 3 Stoke City 0: Valencia, Martial and Lukaku trim gap at the top|
|Shaw feeling on top of his game amid United run|
|Ulster and Ireland wing Bowe to retire|
|Mkhitaryan left out by Manchester United amid Arsenal talk|
|Inter secure Lopez on loan from Benfica|
|Hurst marvels at hat-trick maestro Kane|
|WATCH: Neymar nutmegging for fun in PSG training|
|Best eager to sort out Ireland future|
|Bastareaud and Haskell to learn fate on Wednesday|
|Nantes´ Carlos has red card overturned after being kicked by referee|
|De Villiers leads Proteas´ recovery following imperious Kohli century|
|´Logical´ for Aubameyang to stay at Dortmund, says Stoger|
|Di Resta out of Williams running|
|Stokes ´keen´ for court appearance after affray charge|
|Titans part ways with Mularkey|
|Stupid not to - Giggs seeks Fergie´s advice upon taking Wales job|
|Young hails Wasps´ capture of ´world class´ Sopoaga|
|England all-rounder Stokes charged with affray|
|Nadal expects to get better in Melbourne|
|Suarez feared Chiellini bite would derail Barca transfer|
|Dortmund sign reported Man United target Akanji|
|Short stars again in Hurricanes´ fifth straight win|
|Bangladesh trounce Zimbabwe in tri-nations opener|
|Wales confirm Giggs appointment|
|Barcelona´s Dembele out for up to four weeks|
|Nadal through as five seeds fall in Australian Open first round|
|Williams, Stephens out as American women stumble at Australian Open|
|Wozniacki not getting carried away as seeds tumble|
|Struggling Stoke appoint Lambert|
|Referee suspended until further notice after kicking Nantes´ Carlos|
|Mercedes lead tributes to Gurney|
|Coutinho´s ´deserved´ Barca move, says Figo|
|Toulon stand by Bastareaud after alleged homophobic slur|
|Burgos no match for sensational Nadal|
|Fatigue the issue for goal-shy Chelsea - Conte|
|Wozniacki impresses in first-round triumph|
|West Brom legend Regis dies aged 59|
|Mourinho: I don´t like feuding with managers|
|Venus says she didn´t play bad despite shock Aus Open exit|
|Puel confident of keeping Mahrez at Leicester|
|Valverde: Real Madrid haven´t given up on LaLiga|
|Ibrahimovic nearing end at top level – Mourinho|
|Davis leads Pelicans past Knicks with 48 points|
|US Open runner-up Anderson upset by Edmund|
|Kizzire survives six-hole play-off at Sony Open in Hawaii|
|Venus Williams ousted by Bencic at Aus Open|
|Lakers rookie Ball´s MRI clean, questionable for Monday|
|US Open champion Stephens a first-round casualty in Melbourne|
|Vikings react to ´unbelievable´ win over Saints|
|Steelers QB Roethlisberger plans to return next season|
|WATCH: Diggs´ walk-off TD sends Vikings through to NFC championship|