The Brazilian is set to leave the Blues at the end of the 2019/20 campaign as a free agent, with his seven-year stint looking unlikely to continue.
Willian has been in negotiations for several months over a new deal, however the sticking point has been over the length of the contract.
The Blues are only willing to offer him two years, while the 31-year-old wants a three-year deal to put pen to paper.
Willian has been in decent form since the restart of football, with three goals and an assist in the four games played by the Blues so far.
And while he is has been linked with a move to either Tottenham Hotspur or Arsenal, Lampard hasn’t ended the possibility he will stick in west London.
“I haven’t given up hope on it,” Lampard said. “The club is still in discussions with him. We want him to stay at the club.
“But I also appreciate the fact that this contract for Willian is a big deal for him because of his age and where he’s at. I’ve been there before myself and I respect that.
“But the way he’s playing at the minute shows his worth to the squad and the group and it’s something that I hope we can get to.
“Whatever way with Willian he’s been a great servant to the club and if we can get it I will be happy.
“If not I will certainly wish him well because I’ve got a lot of time for him as a player. In the short-term we can see what he’s doing for us. It’s ongoing.”
If Willian does leave this summer, along with Pedro who is also out of contract this summer, then it will mean a real change up front.
The Blues have already acquired Hakim Ziyech and Timo Werner for next season, while Christian Pulisic and Callum Hudson-Odoi will be looking to impress.
Chelsea have also been linked with Bayer Leverkusen’s Kai Havertz, who has once again impressed in the Bundesliga.
However, Lampard wouldn’t be drawn into whether or not the Blues are in for the Germany international or what their transfer plans might be.
“I’m not completely sure what we’re going to look at in the front line,” he added. “I’ve just mentioned the Willian contract and where that will get to. I’m not sure.
“I certainly don’t want to talk about those things because at the moment we are working towards trying to finish off this season and trying to be better in front of goal in the next five or six games or whatever we’ve got with the FA Cup included.
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“The players can improve and work towards that and we do that all the time. We’ll take a view on that.
“Similarly defensively the players that are here now I have to focus on. What happens in the summer will be what happens.
“I don’t want to talk too far ahead. It’s not the right thing to do. We’ve a got a strong group and we’ve got a job to do. We will sit down and look at it in the summer.”