The 23-year-old believes that his England international teammate is "one of the best left-backs in the world" but is confident of getting the better of him at the Emirates.
"I don't mind scoring against Chelsea," Walcott is quoted as saying by 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."
Walcott added that Cole will be "frustrated" to play against him on Saturday.
"Maybe in the past few years I have had the edge on him," he said.
"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."
Arsenal are currently fifth in the Premier League table with nine points from five matches, four points behind leaders Chelsea.