The England international is in the final year of his contract at the Emirates Stadium with no sign of a new deal on the horizon, sparking numerous rumours that the 24-year-old could be on his way out of the club.
Both Liverpool and Chelsea are said to be interested but, according to the Telegraph, it is the Blues who are growing in confidence that they can complete a sensational swoop.
The Blues have reportedly launched a £35 million bid for the Arsenal star – and are confident that a deal can be done despite the Gunners offering Oxlade-Chamberlain £180,000-a-week to stay at the Emirates Stadium.
According to the report, Arsene Wenger and Arsenal are still fearful that the England international could leave the club after meeting which took place on Thursday – with Chelsea waiting in the wings to take advantage.
Oxlade-Chamberlain made 45 appearances for the Gunners in all competitions last campaign, bagging six goals.