The 23-year-old will have just one year left on his Arsenal contract in the summer and is yet to begin talks over a renewal.
Injuries and mixed form have meant Oxlade-Chamberlain has been in and out of the Arsenal team this season.
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The England international is also yet to nail down a fixed place in Arsene Wenger's starting XI, playing in central midfield and on the wing.
And it is the uncertainty surrounding his career at the Emirates which has lead to Liverpool's interest in the player.
According to The Telegraph, Reds boss Jurgen Klopp is an admirer of Oxlade-Chamberlain and the club are not concerned about Arsenal's high valuation.
Arsenal winger Alex Oxlade-Chamberlain
The German coach is understood to want to grow an English core at Anfield which already includes Adam Lallana, Jordan Henderson, Nathaniel Clyne and James Milner.
Oxlade-Chamberlain is one of several Arsenal players with uncertainty surrounding their futures.
Alexis Sanchez, Mesut Ozil, Jack Wilshere and Kieran Gibbs are just some of the big games with contracts ending in 2018.
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