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, having already agreed terms
The midfielder played the full 90 minutes as the Blues won 2-1 thanks to a stoppage-time header from Branislav Ivanovic.
Goal.com understands that a one-year extension had been agreed with Lampard prior to the Amsterdam ArenA clash.
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"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 all but cap off another dramatic season at Stamford Bridge by lifting a trophy.
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 that his side rode 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."