Lampard, 34, was set to leave the club at the end of the season when his contract expires in the next four months but the Blues are now willing to offer him a new contract.
Lampard, who earns £160,000 a week at Chelsea, is likely to get a wage-cut in his new contract according to Chelsea's policy of not offering improved contracts to players above the age of 30. But that policy was overturned for Ashley Cole, who is believed to offered nearly £200,000-a-weekover a period of 12 months.
Meanwhile, the England veteran scored the winner against Brazil at Wembley and has been in top form in the Premier League scoring 10 goals so this season, just five away from Bobby Tambling's record of 202 for the club.
Chelsea's U-turn to offer Lampard with a new contract has also come from fans pressure against the decision to let him leave.
Lampard has been given permission to negotiate with clubs and has been linked with a move to either China, the Middle East and LA Galaxy. The MLS club are ready to offer Lampard a lucrative two-and-a-half-year contract.
But the veteran midfielder has always wanted to stay at the club and the prospect of playing in the 2014 World Cup in Brazil. England manager Roy Hodgson mentioned there are more chances of selecting Lampard in his 23-man squad if he stays in England.
"I understand where I am in my career, but if I can continue playing for Chelsea then I am getting nearer to 100. It's certainly a target for me and, yes, I will try to keep playing at a good enough level to get there, " Lampard, who has 94 caps for his country, said.
Since joining Chelsea from West Ham United in 2001, Lampard has won three Barclays Premier League titles and helped the club win the UEFA Champions League for the first time in the club's history.