Walcott rates Cole highly but believes he has the edge over his England team-mate, who he got the better of in last season's contest at Stamford Bridge.
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"I don't mind scoring against Chelsea," Walcott told the Daily Star.
"I've done well against them - they must probably hate me, to be honest. "I don't mind playing against Ashley either. I like playing against him.
"He is one of the best left-backs in the world and we have some very good battles against each other - in training as well for England.
"Maybe in the past few years I have had the edge on him. So I am sure when he sees all this he will be frustrated and he will probably want to kick the hell out of me, which is fine!
"He is doing fantastic at the moment and to be that great for so long is an incredible achievement and it is a great honour to play with him."