The 23-year-old has so far refused to sign a new £80,000-a-week contract to remain in north London, with his current deal set to expire at the end of the current campaign.
Walcott's ongoing wage dispute at the Emirates Stadium has alerted attention from a number of Premier League clubs, but Blues boss Rafa Benitez is now believed to be leading the race for the England international's signature.
Liverpool are long-term admirers of the winger-come-striker, and both Manchester City and Manchester United are also thought to be keen on signing him on a free transfer next summer.
Gunners boss Arsene Wenger has refrained from using Walcott as a central attacker, despite the player's positional preference, and Chelsea now hope to lure him to Stamford Bridge in January by guaranteeing him a supporting role to Fernando Torres up front.
Benitez is ready to make room for him by offloading Daniel Sturridge to Liverpool in the New Year, with Brendan Rodgers eager to strengthen his forward options at Anfield in the upcoming transfer window.
As a free agent, Walcott could command a signing-on fee of around £3million, plus wages of £90,000-a-week, so it is likely that he will wait until the end of the season before deciding his future.
A move to Manchester United would see him reunited with Robin van Persie at Old Trafford, but it is almost unthinkable that Sir Alex Ferguson would use Walcott as a striker, given the strength of his options in attack.
The same could be said for Manchester City, who boast Sergio Aguero, Carlos Tevez, Edin Dzeko and Mario Balotelli, though the latter's future at the Etihad Stadium is growing increasingly uncertain as the Italian's relationship with Roberto Mancini continues to strain.