Cole was left out of the 5-0 win over San Marino as Three Lions boss Roy Hodgson opted to give the Toffees star a run out against the international minnows.
And after another impressive showing from Baines, Stuart believes Cole could have a fight on his hands to keep the number three jersey.
He told the Weekend Sports Breakfast: “It was difficult to have a bad game against San Marino but nonetheless Leighton, I thought, was England’s best player on the night. I thought he did terrifically well.
“I think he’s inching closer and closer to Ashley Cole with every passing week, I really do. His performance level for Everton has been outstanding.
“I think Cole has been absolutely magnificent over the years and for the first time in a long time Ashley will have to be looking over his shoulder now because Leighton is coming up strong.”