Moyes has no doubt Chelsea defender Cole is a worthy number one but has been hugely impressed by the progress of Toffees star Baines this season.
The 26-year-old, signed from Wigan four years ago, has taken his game to another level since narrowly missing out on a place in England's World Cup squad last summer.
Moyes said: "I have said many times I think Ashley Cole is the best left-back in England but I think Leighton Baines is just a tad behind him. He needs to keep pushing very hard and improving, he needs to keep continuing his work and get better.
"You can see that Ashley Cole over the years has kept going but I think Leighton Baines has been the 'big mover'. He has done really well.
"I think he is getting closer to Ashley but in my personal opinion I think Ashley Cole is probably still England's best left-back."
Source: PA
Source: PA