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."
|Rallying Tsonga outlasts Shapovalov in five-set epic|
|Wozniacki saves two match points in dramatic Aus Open comeback|
|Kostyuk, 15, ready to spend after Melbourne run|
|Thomas turns down Celtics´ video tribute|
|Moyes unaware of Chelsea interest in Carroll|
|Verdi wants Bologna stay amid Napoli links|
|Ronaldinho retires – A shining light of Brazil´s 2002 World Cup-winning team|
|Ronaldinho retires – a World Cup and Ballon d´Or among Brazil great´s prizes|
|Celtics great White dead at 71|
|World Cup glory and Bernabeu magic - Ronaldinho´s best moments for Barca and Brazil|
|Trust the Process – 76ers only behind Warriors and Cavs in merchandise sales|
|Ligue 1 Review: Balotelli at the double as Payet shines and Malcom toils|
|Pato still dreaming of World Cup selection|
|FA Cup Review: Iheanacho makes VAR history, kit confusion reigns|
|Wallaby saves wallaby: Farr-Jones in Sydney Harbour Bridge rescue mission|
|2016-17 UEFA Study: PSG, Man City drive record-breaking spending|
|Conte packing in homework as Chelsea games stack up|
|2016-17 UEFA Study: The headlines in transfers, wages and revenues|
|2016-17 UEFA Study: Manchester United record highest revenue but largest debt|
|Monaco stay perfect, Murcia overcome Oldenburg|
|Iheanacho scores English football´s first VAR goal|
|Materazzi not surprised by Coutinho transfer fee|
|Ronaldinho retires - Brazil and Barca great plans 2018 farewell|
|Jags RB Leonard Fournette uninjured in three-car accident|
|India revenge would heal Proteas´ scars - Elgar|
|Koziello swaps Nice for Cologne|
|Simeone ready to unleash Costa and Vitolo alongside Griezmann|
|Head coach Cooper to leave Stade Francais|
|Silverwood plays down talk of replacing Bayliss|
|Lambert ´never thought´ he would return to Premier League|
|Wenger ´very aggressive´ towards referee Dean, says FA report|
|Reported Arsenal target Malcom starts for Bordeaux vs Caen|
|Valverde not making big deal of Dembele´s latest Barca blow|
|Costly day for Kohli as Proteas close in on series win|
|Date set for Afghanistan´s maiden Test|
|Returning McIlroy ready to end winless run|
|In-form Short leaves coach Kirsten needing dental treatment|
|Arsenal will have a ´hard time´ signing Malcom|
|Ronaldo and Madrid nominated for Laureus awards|
|Nantes´ Diego Carlos brands Chapron clash ´historic´|
|This is not important - Conte unconcerned if substitutions upset Hazard|
|Conte ´doesn´t think´ Chelsea have pursued Sanchez|
|Cobblestone climb part of 2019 Tour de France Grand Depart|
|Emery hints at Neymar return against Dijon|
|Joshua labels Parker claims ´fake news´|
|´Emotional´ Fleetwood honoured by Seve Ballesteros Award|
|Tears for Kvitova as Bouchard sets up Halep meeting|
|Mkhitaryan key to United-Sanchez deal, claims Raiola|
|WATCH: Sabalenka wins point using racquet throat|
|Federer, Djokovic and Zverev among Australian Open first-round winners|
|Kubica gets reserve role as Williams hire Sirotkin|
|Shambolic Stars out after Sixers thrashing|
|Wales pick uncapped Worcester wing Adams in Six Nations squad|
|Tevez: CSL spell was a holiday|
|Mignolet considering Liverpool future|
|Laidlaw among several returning stars in Scotland Six Nations squad|
|´Fairy tale´ 2017 motivation for Federer|
|Fred waiting for Guardiola call amid Man City speculation|
|Dominant Federer makes light work of Bedene|
|Halep faces nervous wait over ankle injury|
|Inter confident but patient over Rafinha|
|Kohli fined after umpire outburst|
|Djokovic hits back at Australian Open boycott suggestions|
|De Grandhomme lifts Black Caps to win in Taylor´s 200th ODI|
|Giggs had counselling after Old Trafford exit|
|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|