The 24-year-old had been thought to be on the verge of a £35m switch to the Premier League champions after Arsenal had agreed a fee with their London rivals.
However, Sky Sports News reports that Oxlade-Chamberlain has rejected a move to the Blues and will now either stay at the Emirates Stadium or join Liverpool before Thursday's transfer deadline.
Liverpool have been repeatedly linked with the England international throughout the summer but are yet to table a formal bid.
Oxlade-Chamberlain's contract at Arsenal expires at the end of this season and he will be able to leave on a free transfer next summer if no new deal is agreed.
Arsenal boss Arsene Wenger has repeatedly insisted that Oxlade-Chamberlain will not be sold during the current transfer window, but the player himself is keen to leave.
Oxlade-Chamberlain, who was part of the Arsenal side that was put to the sword by Liverpool on Sunday, has scored 20 goals in 198 appearances for Arsenal across all competitions.