The 34-year-old, who played the full 90 minutes as the Blues stunned Benfica in stoppage time, is expected to sign a one-year extension.
The midfielder played the full 90 minutes as the Blues won 2-1, thanks to a stoppage-time header from Branislav Ivanovic.
And after the game, Lampard - who broke the club's goals record against Aston Villa on Saturday and had been linked with a move to MLS - hinted that a contract extension is close to completion.
"We are getting there," he told ITV. "With the game tonight and the game on Sunday we haven’t sat down to really complete it yet but the club have been brilliant so it looks good."
The 34-year-old was also delighted to lift another trophy after a dramatic season at Stamford Bridge.
He added: "It has been an amazing time for all of us. The last two years - talk about some ups and downs. There’s been some big ups and this was another one."
Lampard also conceded his side was able to ride out the storm in Amsterdam as Benfica dominated for long spells.
"We are fortunate but you make your own luck," he said. "It’s been a long season, but we’ve stuck together along with the fans and the club deserves it."