The Sunday Mirror says Lampard has developed a close working relationship with manager Jose Mourinho, who wants to keep him at the club.
Terry and Cole are out of contract in the summer and could leave.
Cole is a near-certainty for England’s World Cup squad, but is no longer Mourinho’s first choice.
Terry wants a two-year contract from Chelsea and that is unlikely. He may have to settle for a new one-year deal if he wants to stay.