Lampard, who scored the winner for England in last night’s 2-1 victory over Brazil, had been told he could leave Chelsea at the end of the season.
Incredibly, Chelsea made their move for the fans’ favourite last week and talks about him staying are at a preliminary stage.
Sources at Stamford Bridge insisted this morning that the talks were ‘positive’ and the club will formalise the fresh talks with a firm offer.
The precise terms of the new deal for Lampard, 34, have yet to be discussed, but the initial meeting with Chelsea has taken place.
Abramovich, who is in Malaga on business, is aware of the fans’ protests against the decision to release the midfielder after 12 years at the club.
Lampard has scored 10 goals in just 17 Barclays Premier League appearances this season after recovering from injury.
He is now second in the list of all-time leading scorers at the club and is just five goals from equalling Bobby Tambling’s record of 202 in a Chelsea shirt.
The midfielder has been one of the club's most consistent players this season and supporters have begged Abramovich to give him a new deal.
Chelsea’s owners is becoming increasingly sensitive about his popularity at the Bridge and is determined to put his club back at the top of European football.
That process began when he changed his mind about Ashley Cole and gave England’s left back a new one year extension to his contract.
Lampard is next in line and talks are expected to resume within the next week after
Chelsea made their shock move to keep him. A Chelsea spokesman declined to comment this morning.
Lampard’s future is time sensitive because he already has a number of offers from other clubs around the world.
Paris Saint-Germain, coached by former Chelsea manager Carlo Ancelotti, are the latest club to put down a marker for the midfielder.
LA Galaxy, who have offered Lampard a two-and-a-half year deal, are pushing for an answer. The MLS season starts in March, but the player will have commitments with Chelsea until the end of the season and also with England.