Jose Mourinho is drawing up plans to strengthen his midfield ahead of the transfer window opening on July 1 and the Red Devils are monitoring the situations of both players, who have contracts expiring in less than 15 months time.
Oxlade-Chamberlain, 23, has been heavily linked with a move away from Arsenal this summer after six years at the club.
Despite an evident improvement in his performances on the pitch during the current campaign, the England star has only managed to score three Premier League goals in his last two seasons at the Emirates and an offer of a contract extension has yet to be put on the table.
Mourinho previously tried to sign Oxlade-Chamberlain as part of the deal which brought Petr Cech to Arsenal in 2014. The swap request was rejected by Arsene Wenger and Cech's move to north London ended up being eventually sanctioned by Chelsea owner Roman Abramovich, who overruled the Portuguese coach.
His versatility is a key attribute as to why Mourinho wants to bring him to Old Trafford, with impressive performances in a central midfield role for Arsenal exemplifying what he could add to an area of weakness.
United’s recent game against Middlesbrough without Paul Pogba and Ander Herrera in midfield left Mourinho having to choose from Michael Carrick and Marouane Fellaini, and the addition of Oxlade-Chamberlain would go some way to easing their depleted midfield.
Meanwhile, contract talks with Ozil will resume at the end of the season after both parties failed to reach an agreement over an extension. The Germany international is happy in London but talks have not progressed as expected, with one source telling Goal that protracted negotiations have turned into a ‘game of poker’.
Goal understands that Ozil has no intention of relocating from London to Manchester, however, which puts any potential move into huge doubt. Talks will continue at the end of the season and it's likely that the future of Wenger will have a bearing on his final decision.
Ozil has struggled to replicate his outstanding form from last season, where he created more chances in a single campaign than any other player in Premier League history.