Lampard's contract situation has been the subject of speculation since the start of the season with his current deal set to expire this summer.
For a long time it seemed as if Chelsea were prepared to let Lampard leave on a free transfer at the end of the season, but the report claims the Stamford Bridge hierarchy are now ready to extend his contract on similar terms to his current deal.
An official announcement is not expected until the summer when Chelsea appoint a new manager to replace interim boss Rafa Benitez.
Real Madrid boss Jose Mourinho is the favourite to take over, and he would be reportedly keen to keep Lampard on board. The report even claims Mourinho would be willing to announce Lampard's new deal at his first Stamford Bridge first conference.
Speculation regarding Lampard's future at Chelsea had prompted rumours of a move away from Stamford Bridge, ending a 12-year association with the club he joined from West Ham.
Manchester United were one surprise name in the frame, while LA Galaxy were another mentioned with a potential interest in the England man's availability.
But Chelsea will insist the decision to offer Lampard a new deal does not represent a u-turn, but rather properly reflects their desire to complete contract business at the end of the season.
After scoring his 201st Chelsea goal at Stamford Bridge last weekend, the 34-year-old midfielder is just one short of Bobby Tambling's all-time club goalscoring record.