City remain very keen to sign Sanchez from before Deadline Day ends, though, and will improve on that initial offer.
And 24-year-old admits the decision to leave Emirates Stadium did not come easily.
Personal terms will now be discussed with reports suggesting Oxlade-Chamberlain could undergo a medical on Wednesday evening at St George's Park - where he is currently training with England ahead of their World Cup qualification double-header.
Oxlade-Chamberlain's exit looks inevitable; it is now just a matter of where he goes.
This is believed to be the reason for Jurgen Klopp bringing the player from London to Liverpool.
Sharapova drops 1st set in 2nd round at US Open
Asked about her low points, Sharapova , said, "There were definitely a few but I don't think this is the time to talk about that". She looked particularly nervous in the tiebreak, losing it 7-4, but ended up hitting 39 winners to 36 unforced errors .
"There's still Coutinho and Lallana to come back, players who performed so well".
I'm here with England and we've got two big games coming up, so I want to focus on them. But, like I say, if you said to me a year ago, or six months ago, you would get £40m for Oxlade-Chamberlain, I would've snapped your hand off.
"That's a brilliant deal to get".
Sky sources understand Oxlade-Chamberlain will earn a minimum of £120,000 a week at Anfield - a figure which could increase with win bonuses and loyalty payments. "But Liverpool will take him out of his comfort zone".
Oxlade-Chamberlain was part of that famous "British core" photo when he signed a new contract together with Jack Wilshere, Aaron Ramsey, Kieran Gibbs and Carl Jenkinson in 2012.