Oxlade-Chamberlain was touted as a target for Jurgen Klopp in April, with the German eager to add the versatile England international to his squad.
However, speculation over a possible bid for the 23-year-old had faded in recent months, with Oxlade-Chamberlain instead suggested to be set to stay in north London.
Chelsea were also believed to be a more likely destination for the midfielder, as Antonio Conte seeks reinforcements.
But according to the Mirror, Liverpool are now due to make a “huge push” to sign Oxlade-Chamberlain before August 31.
This comes after he turned down a lucrative £180,000-a-week contract to stay with the Gunners, underlining his ambition to move on in search of regular first-team football.
They will reportedly only consider offers of around £35 million, however, which four months ago was reported to be over Liverpool’s valuation.
But given their lack of success elsewhere in the market—with a big-money move for RB Leipzig mdifielder Naby Keita failing—Klopp’s side may be more willing at this crucial stage.
Speaking ahead of Sunday’s clash with Arsenal at Anfield, Klopp intimated that he was still looking to add to his squad this summer.
“We work on it, you can imagine. We are in talks. Will something happen? I don’t know,” he told reporters.
“Obviously this transfer window is different to all other transfer windows.
“We will see what happens. I’m happy at the moment. Will I be happy on 31st still? Not sure. Will I be happier? Possible—we will see.”
Oxlade-Chamberlain is now expected to be left out of Arsene Wenger’s squad for the trip to Merseyside, having told the Frenchman he wishes to leave the club.