With Chilwell playing inconsistently at Stamford Bridge, Cole thinks Shaw is number one at the moment.
Speaking on ITV, Cole said: "I think at the moment Shaw is in the lead.
"It is a tight one but I think Shaw is just pipping it at the minute. I think he is playing more consistently for Manchester United, where as Chilwell . . . some days he plays and some days he does not [for Chelsea].
"But who knows? Going into the last games of the Premier League season, who can hold their nerve and keep that consistency up before the squad gets announced?"