Oxlade-Chamberlain, 23, has just 12 months remaining on his Arsenal contract and faces an uncertain future at the Emirates.
The Gunners are keen to hand the England global a new deal, but talks have apparently broken down.
Oxlade-Chamberlain has been mainly used as a winger at Arsenal and has also been deployed in a central midfield role but he really impressed in the wing-back position when Wenger switched to a 3-4-2-1 formation during the second half of last season.
According to Sky Sports reporter Kaveh Solhekol, as seen in the tweet below, despite the two players in question being linked with different moves, it's claimed that Arsenal could be willing to swap Oxlade-Chamberlain in exchange for Matic.
Matic, 28, is at risk of dropping down the pecking order at Stamford Bridge. Monaco midfielder Tiemoue Bakayoko appears to be the club's third signing ahead of the 2017/18 season, but an official deal with the Blues has yet to be announced.More news: Target's stock jumps after raising sales, profit outlook
Costa has not reported back for pre-season training this week, after he was given permission to extend his holiday, as he tries to seal a move back to Atletico Madrid.
And Di Marzio seems to think Arsenal are keen to capitalise on this uncertainty.
It is said the player himself wants to join the Red Devils, but a deal is being complicated due to the arrival of former Blues striker Romelu Lukaku from Everton.