The Sun says Blues boss Rafa Benitez is confident of getting his man as the £15million-rated winger would not have to uproot from London.
But Chelsea have sent a scout to watch Walcott — and plan to use him as a more central attacker, a role the England man craves.
Interim boss Benitez will have cash to spend in next month’s transfer window.
He rates Walcott’s lightning pace as a huge asset as he looks to land a player to support Fernando Torres.
The forward, 23, has refused to sign a new £80,000-a-week contract at Arsenal — and can leave for nothing next summer when his current deal runs out.
The Gunners know they could still raise around £15m for the player by selling him in January.
Walcott is likely to try to wait until the summer before moving.
As a free agent he could command a signing-on fee of around £3m plus £90,000-a-week wages.