The Sunday Mirror says the 63-times capped Newcastle legend has his sights set on club rather than country as he prepares for a move into management.
A source said: "Alan is flattered that he is being linked with a role alongside Capello in the England set-up. He admires Capello and knows it would give him the chance to learn from a top coach.
"But there have to be doubts about how he would fit in with a largely Italian staff and whether it would ever lead to anything other than a coaching role.
"Alan has always been a leader of men and his ambition since doing his badges is to be in sole charge of a team. That's why he will take his time and weigh up his options."