Willian’s current contract will expire at the end of the 2019/20 season, and he will be free to negotiate with foreign clubs from January 2020.
The 31-year-old has been pivotal as Chelsea have embarked on a six-game winning streak that has catapulted them to third on the Premier League table.
Willian was handed the captain’s armband and laid on a sublime assist for Tammy Abraham in Chelsea’s 2-0 win over Crystal Palace last Sunday.
Lampard played with Willian in his final season as a player at the club and believes it is paramount to tie him down on fresh terms to guide a side saturated with youngsters.
"The word isn't 'no-brainer' because I can't get involved in the money. That's up to the club to do," Lampard said.
"But everyone sees how much I'm relying on him and picking him and, in what he is producing, I love him at this football club. So there's my answer.
"I know his qualities from playing with him but when I looked at Willy over the last couple of years, he was in and out of the team. You're not sure, from the outside [what's happening]. I want to see him happy.
"Willy is a happy, easygoing lad who loves his football and that was the first thing I said to him at the start of the season.
"I saw him being huge in the way I wanted to play. Naturally, on the ball, we all know his ability to go by [markers] one-v-one and shift people and cross or get shots away.
"But his off-the-ball work is an outstanding example for Callum Hudson-Odoi, for Christian Pulisic, for other young players who think the only part of the game is going by people, crossing or shooting."
"He does the other side brilliantly with absolute humility. He's been a joy and one of the experienced players who is helping the young boys."
The former Shakhtar Donetsk man was heavily courted by Barcelona last summer but Chelsea repeatedly rejected a series of bids from the Spanish champions.
Chelsea stole Willian from the clutches of Tottenham Hotspurs, where he had undergone a medical, for a fee of £30m from Russian side Anzhi Makhachkala in the summer of 2013.
Willian has won two Premier League titles, one League Cup, one FA Cup and recently added the Europa League to his trophy collection in London.
Willian has made 15 appearances in all competitions for Chelsea this season, recording three goals and three assists.
