The midfielder scored twice to lead the Blues to a 2-1 victory over Everton but insists that he is simply concentrating on his football despite the speculation surrounding him
Returning to Chelsea's starting XI, Lampard saw his team go one goal down in the second minute to a Steven Pienaar strike before scoring a goal either side of half-time to push them back into third place.
The victory marks a fourth successive Premier League win for Rafael Benitez's team but speculation continues to surround Lampard's future, with the 34-year-old midfielder eligible to sign a pre-contract agreement with foreign clubs from January.
"I just hope [the New Year] brings me playing in a winning team," he told Sky Sports. "I keep trying to give my best like I've always done here and I'll continue to do so.
"I'm enjoying playing, I was injured for a while and I know there's a lot of speculation and talk but for me, it's all about the 90 minutes there."
He added to the BBC: "We haven't been talking [about a new contract] in the last couple of weeks and I'm just concentrating on playing. Playing games gives me enough satisfaction, then what will be, will be."
Lampard reserved praise for the Blues supporters, who urged Benitez to "sign him up" - in reference to his expiring contract - during Sunday's clash on Merseyside.
"They've been amazing and they are the club," he continued. "From the minute I came here, I've said it a million times - they've been behind me and I've always got Chelsea in me for life.
"They back their team and they back all the players in the team at every match, so I can't thank the club enough."
The two goals Lampard scored put him just one goal behind the club's second all-time top scorer, Kerry Dixon, and earned the commendation of Benitez.
The former Liverpool boss would not be drawn into commenting on the midfielder's future beyond the term of his current contract, however, which expires at the end of the season.
"I am really pleased with the team, credit to Frank for the goals," the Spaniard said. "Lampard is a great player, a good professional, who is doing well for us and I will try to bring the best out of him until the end of the season.
"He is one of the players who if he gets in the box he can be dangerous. He is under contract. He has shown his full commitment.
"He is a great player and my job is to keep him fit, happy and scoring goals. If he can score goals every game I'll be pleased."