The Daily Star says talks continued yesterday to seal a one-year deal.
Manager-in-waiting Jose Mourinho has persuaded owner Roman Abramovich to reward the club’s record scorer with a new contract, similar to the one fellow England star Ashley Cole signed earlier in the season.
It is understood Lampard’s agent, Steve Kutner, was yesterday still trying to net the best possible terms.
But the midfielder made no secret at wanting to stay at Stamford Bridge.
Yesterday a source close to Mourinho, who will quit Real Madrid at the end of the season, said simply: “Lampard stays.”