Both Manchester clubs have been linked with a move for the Chilean.
Arsene Wenger: Alexis Sanchez will not be sold by Arsenal until replacement is found
Alexis Sanchez will only be sold this month if Arsenal can find a replacement, manager Arsene Wenger has said.
Sanchez, out of contract at the end of the season, is expected to leave the north London club during the transfer window with both Manchester City and Manchester United in the race to sign him.
The 20-year-old Brazilian forward Malcom - who has netted seven times for Ligue 1 side Bordeaux this season - has been linked with a move to the Emirates Stadium to fill Sanchez's boots.
And Wenger, whose side travel to Bournemouth on Sunday as they return to Premier League action, admitted that the Chile international will only be allowed to leave if they can get a new signing over the line.
The Frenchman said: "Of course I want a quick resolution.
"Is he [Sanchez] replaceable in the way that we find exactly the same player? Certainly not, but there's always a way to find a different balance.
"Alexis is an exceptional football player, he's a world-class player and if that happens [and he leaves] we have to find a different balance in the team.
"I have had many conversations about him and we talked about the fact that people are always observing you with a microscope when you're on a short-term contract, but I've never questioned his professional attitude when he's on the football pitch."
Reflecting on United's reported interest in the former Barcelona forward, Wenger added: "A bidding war is always beneficial to the club who can take advantage of it. We are not in that.
"I maintain what I've said many times. Normally, he should stay here until the end of the season but we'll see."
Theo Walcott is another Arsenal player poised to leave this month with Everton manager Sam Allardyce revealing on Friday that they are hopeful of sealing a permanent deal.
Wenger said he does not want the 28-year-old to leave, but conceded he cannot guarantee the forward playing time and an unlikely route into Gareth Southgate's England squad for the World Cup.
"Sam Allardyce has made that statement but Theo Walcott is here," Wenger added.
"I have a good relationship with Theo and I don't want him to be frustrated or lose an opportunity to go to the World Cup.
"Theo went to the World Cup in Germany in 2006 and we are now in 2018 and since then he has not been for different reasons, so that is a sensitive subject."
Mesut Ozil, who is also out of contract at the end of the season, is battling a knee problem and is rated as only "50-50" for Arsenal's trip to the Vitality Stadium.
Midfielder Aaron Ramsey is back in the squad following a hamstring injury, while Jack Wilshere, who hobbled off with an ankle issue against Chelsea on Wednesday, could also feature on the south coast.