With Ashley Cole a doubt for the finals after ankle surgery and Wayne Bridge having ruled himself out of contention, Capello is having to reassess his options at left-back.
Baines and Aston Villa's Stephen Warnock appear to be top of the pecking order and should be tested by Capello in next week's friendly against Egypt.
Baines is uncapped - he has twice been called up by his country, for a friendly against Slovakia and a World Cup qualifier against Ukraine, but remained on the bench. But has excelled at club level over the past couple of seasons.
And Moyes feels the 25-year-old has all the attributes to be a success for England this summer. He said: 'Leighton will get spoken about because he will be one of the next in line for the spot. Probably Leighton and Stephen Warnock are the names that are being thrown in and I am sure the manager of England will have a look at them in the weeks and months leading up to the World Cup. I think since Bainesy has come into the side he has improved and has kept improving. Sometimes there is one like that who comes into the World Cup squad late on and does very well. I am hoping it's Bainesy because he has done very well for us here at Everton.'
Moyes believes Baines is comparable to Cole in terms of his style of play and ability, adding the former Wigan defender is the ideal modern full-back.
'He is a very good attacking full-back,' Moyes said. 'He's quick, hard to get past as a defender and he is good on the ball. He has varied talents. But I don't pick the England team, it's hard enough picking the Everton one.'