The 34-year-old's current deal is up at the end of the season, and until recently there appeared little prospect of a new one.
But it emerged recently his form had forced Chelsea to rethink, and chief executive Ron Gourlay said: "Discussions are ongoing and must be kept confidential at this stage."
Lampard has scored 10 Premier League goals for the 10th consecutive season and now has 199 for the club - just three fewer than record scorer Bobby Tambling.
Captain John Terry last month led the calls for Lampard to stay, describing his team-mate as "an inspiration to everyone at the club".
And Lampard recently hinted he would be happy to remain despite his number of starts dwindling this season to just 15 in the league.
Speaking last month about his chances of going to the 2014 World Cup, he said: "I'm very understanding of where I'm at in my career.
"But if I can continue playing for Chelsea and continue contributing here, whether it's starting or as a valuable squad member, then the World Cup is getting a bit nearer."