The England international, 28, made 29 appearances in all competitions last season but featured just seven times since the turn of the year.
He was left out of Liverpool's matchday squad for seven of their last eight games in the final weeks of the Premier League season, with his last appearance coming against Nottingham Forest in the FA Cup on March 20.
Reports claim Oxlade-Chamberlain will be allowed to leave Anfield this summer if a suitable offer arrives.
According to talkSPORT's Alex Crook, Manchester United are considering a surprise bid for the former Arsenal midfielder.
United need to sign midfield reinforcements after allowing Paul Pogba, Jesse Lingard, Juan Mata and Nemanja Matic to leave at the end of their contracts.
The report claims United would be 'seriously interested' in bringing Oxlade-Chamberlain to Old Trafford if Liverpool are willing to accept a knockdown fee of £10m.
Oxlade-Chamberlain’s former club Southampton are also interested in the midfielder but have concerns over his injury record and wage demands.
Should Oxlade-Chamberlain join United this summer, he would become the first player to transfer directly between the Red Devils and Liverpool in more than half a century.
The last player to move between the two clubs was Phil Chisnall, who joined Liverpool from United in £25,000 transfer in 1964.
Oxlade-Chamberlain first joined Liverpool in a £35m move from Arsenal in 2017.
He has gone on to score 20 goals in 198 appearances for the Reds, winning the Premier League, Champions League, FA Cup, Carabao Cup and Super Cup during his time at Anfield.
However, he now looks destined to leave the club this summer after falling down the pecking order in recent months.
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