And he insists a better option would be to keep Maurizio Sarri in charge for at least one more year after a successful season for the west London side.
"Sarri, for me, has done very well," Poyet said to TalkSport.
"I know we talked earlier in the season about the style of football, about Sarriball, blah, blah, blah.
"But at the end of the day, he finished third behind the two best teams for many, many years in the Premier League, he won the Europa League and was in the final of the League Cup, which they lost on penalties. So it wasn't that bad.
"I'm not sure whether it's Chelsea that want him to leave, or he himself wants to leave.
"It looks to me that he's had enough of the criticism for the job he's done and actually he is the one who wants to leave.
"Me? I want Sarri to stay.
"Having the results they've had, I think it's a good option to have him for another year. But I've got a feeling that it's him who has had enough. I hope not, though."
However, Poyet did admit he would think that it would be a difficult opportunity for Lampard to turn down.
"I think it's a beautiful job and, if he has the chance, Frank has to jump at it," added the former Blues midfielder.
"It's a rare opportunity, and it's a good option. He knows the club, he knows the politics inside the club, and he knows you need to have a different way of playing."