The deal was earlier reported by Sky Sports on Monday.
The 24-year-old will provide Chelsea with depth at wing-back and at the central and attacking midfield positions if a transfer is completed before the window closes on Thursday.
Oxlade-Chamberlain is in the final year of his contract, but Arsenal coach Arsene Wenger had been resistant to let the England international leave this summer.
Wenger said two weeks ago that he wanted to keep both Oxlade-Chamberlain and Jack Wilshere at Arsenal this season, even if it meant losing both on a free transfer next summer.
“I rate him highly and he’s one of the players who is on his way up,” Wenger said of Oxlade-Chamberlain on Aug. 16. “In the last year, he has made huge progress and personally I want him to stay here for a long time.
“I’m convinced he will be the English player that everybody will look at in the next two years.”
News of a move comes with Wenger again under pressure following a 4-0 trouncing at Liverpool on Sunday, in which Oxlade-Chamberlain started but was replaced by new signing Alexandre Lacazette after an hour.
Meanwhile, other sources told ESPN FC that England coach Gareth Southgate is relaxed about the timing of deals being done, despite his squad set to fly to Malta hours before the transfer deadline.
Southgate would rather his players’ club matters be settled ahead of next summer’s World Cup, sources said, and though any move late this week could jeopardise a player’s ability to face Malta, there will be no formal deadline from the Football Association.
Premier League champions Chelsea have also been strongly linked with moves for Leicester’s Danny Drinkwater and Everton’s Ross Barkley, neither of whom were named in Southgate’s squad last week.