Carrick fell out of favour under former England manager Fabio Capello, and although he was a member of the Three Lions squad at the 2010 World Cup, the West Ham United youth graduate did not feature in South Africa.
Roy Hodgson was appointed as Capello’s successor in May but Carrick was omitted from the 23-man travelling party for the European championship.
The England boss wanted the midfielder to be on the standby list, but the midfielder declined Hodgson’s offer, and Jordan Henderson was drafted into the squad to replace the injured Frank Lampard ahead of the tournament.
“I’ve had no contact from Roy Hodgson, so it would be wrong of me at this stage to make a decision either way,” said Carrick. “But I would consider it, definitely.”
Carrick, who has won four Premier League titles and the Champions League in 2008, defended his decision to reject Hodgson’s offer to go on England’s standby list.
The former Tottenham Hotspur midfielder admitted he found the experience of going to the last World Cup but not playing a single minute very difficult.
“I didn’t kick the door down and say: ‘You’ve got to play me or I’ll leave’,” he added.
“It wasn’t a case of that at all. It was more that if I wasn’t going to play, I’d rather not go.
“During the World Cup I never featured and I was never really close to playing. That was a hard time. I just thought if it was going to be the same scenario again, I’d rather let someone else go in my place.
“It’s a game of opinions and Capello wanted to play a certain way. If that was the road he wanted to go down, it wasn’t for me to argue with that. I just didn’t play, that’s all.”
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news