However, it looks as though Liverpool could be beaten to the punch as the Daily Star claim that after seeing their initial £25m bid rejected by Arsenal, Chelsea have now tabled an improved £35m offer for The Ox.
Oxlade-Chamberlain could feature for Arsenal when the Gunners take on Leicester City in their Premier League opener on Friday night.
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The report suggests Chelsea's presence in the Champions League - along with a potential pay-rise at Stamford Bridge - could be two key factors as Oxlade-Chamberlain weighs up his future move.
Sportsmail understands Chelsea have stepped up their interest in the England global over the past week.
The £25million rated ($32.5million) rated former Southampton player has also been wanted by Liverpool this summer with Jurgen Klopp a huge admirer (Mirror).
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Antonio Conte has been promised at least three more new faces and needs homegrown players for Chelsea's quota. "Last year he was much more stable". The 23-year-old is a favourite among fans and fellow team-mates and a departure from the Emirates would be devastating for the club.
'He is today very conscious of his qualities as well, which he was not always, and I personally believe he will be a very great player'.
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He added: "We are still open". "We were never close", he said, when asked about Arsenal moving for Mahrez. Leicester value him at around £50m ($69.4m ) and no clubs have managed to meet their valuation thus far.