Cole is facing disciplinary action from Chelsea and the FA after he reacted furiously on Twitter to doubts being expressed about his evidence in the John Terry racial abuse case.
The Chelsea full-back is in Roy Hodgson's squad for the forthcoming World Cup qualifiers against San Marino and Poland but some pundits, such as former England striker Alan Shearer, have called for Cole to be banned.
Shearer told the BBC: "I think the FA can put a big statement out here by not fining him but actually banning him on Friday against San Marino."
Cole responded by retweeting a comment on Twitter which referenced an incident in the game between Newcastle and Leicester in 1998 when the former Magpies forward's boot made contact with Neil Lennon's face.
The FA ruled the striker had been making a "genuine attempt to free himself" from a tangle with his opponent and took no disciplinary action against him.
Cole retweeted a post from @CollinR4 which read: "Alan Shearer says @TheRealAC3 needs to be banned for comments. I want his opinion on bans for kicking Neil Lennon in the head. #GlassHouses"
Cole has spoken to Hodgson and will meet up with the squad at the new national football centre, St George's Park near Burton-upon-Trent, on Monday.
It is understood that if he is left out of the San Marino match it will be a case of Hodgson resting players against the Group H minnows rather than any statement relating to the controversy that erupted on Friday.
Cole, 31, has 98 England caps to his name and will be desperate to reach the 100-mark.
He will also be part of the England squad that assemble at St George's Park for the official opening on Tuesday by the Duke and Duchess of Cambridge, William and Kate.
Cole called the FA a "bunch of t***s" on Twitter after he was accused of "evolving" his statement supporting Terry's defence against the charge he racially abused Anton Ferdinand.
Chelsea boss Roberto Di Matteo confirmed the left-back would be punished by his club.
Di Matteo said: "We've got a social media policy at the club and there's going to be a disciplinary process - action - against the tweet and that's how I'll leave it."
The Italian added: "The image of the club is very important to us of course.
"We have rules, and anybody who breaks the rules faces disciplinary action against them.
"We strive to have high standards and hopefully, going forward, we can be better at showing those.''
``I come from Switzerland so I like rules, and rules are there to be respected.
"I wouldn't say I'm a disciplinarian but, when you live and work in a group environment, you need rules to be able to live together and work together.''