Arsenal agreed a £40m transfer fee with Premier League champions Chelsea but Oxlade-Chamberlain has his heart set on a move to Anfield.
The Gunners have turned down a £30m offer from Liverpool but the bookies believe a deal will be struck.
Coral spokesman John Hill said: “The betting suggests Alex Oxlade-Chamberlain’s most likely destination is going to be Liverpool as he is odds-on to join up with Jurgen Klopp’s squad before the summer transfer window closes.”
Oxlade-Chamberlain is 6-4 to remain at Arsenal and 5-1 to join Chelsea.
The England international has one year left on his current contract.
He has refused an extension, despite being offered £180,000-a-week.
Chelsea boss Antonio Conte fancies using Oxlade-Chamberlain at right-wing-back.
But he wants to move into a central midfield role, which is more likely at Liverpool.
Arsenal are willing to sell Oxlade-Chamberlain to Liverpool, despite the bad blood between the two clubs.
They fell out when Arsenal bid £40m plus £1 for Luis Suarez in 2013 to trigger a release clause in his contract.
