The 31-year-old has been charged by the FA with misconduct after posting an offensive tweet criticising the governing body.
When asked if he is worried whether Cole has been badly affected by the situation, Jagielka told the London Evening Standard: "No not at all. Ash has been fully focused all week. He is professional, you have to be to have done what he has in his career.
"He is desperate to play in Poland and if the manager picks him to play he will be fully prepared. I've got no doubt he will do a fantastic job, just like Baines if he gets selected.
"I'm a big fan of Ashley. I have been fortunate to play with him on a number of occasions with England. What is so remarkable about him is his consistency, how many years he has been playing at such a great standard and how much effort he puts into every game he plays in.
"People forget how hard it is to get to 98 games for your country - that takes being in lots of squads, putting up many good performances and beating off many people who are trying to take your place.
"Ash has done fantastically well at club level to keep himself as England's left-back and it is going to be a tough call because Baines is doing so well at the moment but it's a nice decision for the coach to have to make."