The 34-year-old midfielder might be just two goals shy of the Blues' all-time scoring record, but a Stamford Bridge exit at the end of his contract this summer looks likely. Having stayed on the bench for Sunday's FA Cup semi-final with Manchester City, Lampard is in line to make his 600th Chelsea appearance at Craven Cottage.
Fulham boss Jol was full of praise for the England international ahead of the match but dismissed suggestions he might make a summer approach, and the Dutchman said: "He will have a smile on his face if he listens to Fulham but I would love to have him. But it's hypothetical as he will never play for Fulham. I'm not sure he will play for a top-10 team."
He added: "He is the most productive midfield player in England in the last 30 or 40 years. Everyone would love to have him. He's fit and is a good character.
"He's a legend - a living legend over there. He won all the prizes over there. In the end I have a feeling they will keep him."
Any move for Lampard would fly in the face of Jol's ambition to lower the age of the Fulham squad. They have had the oldest in the Premier League for the past three seasons, but the Cottagers boss will not use young players for the sake of it.
"Necessity is the mother of invention," he said. "I've got a few youngsters but they have to do well. For example Matthew Briggs is a youngster and has played for a few loan teams but he has to do well. If you don't do well you can't expect to be in the first team.
"Kaca (Alex Kacaniklic) did okay but they have to work hard and develop themselves. Kerim Frei is one them. Chris David will be one of them but they have to prove they are as good as someone in the first team.
"It's not an easy one but I'm 100 per cent certain that we have one of the best academies in England. They proved that every year - champions of England and finalists before.
"How many players in England are 18 or 19 in the first team? Mention one player. But Fulham will have one or two. I am always respectful for my older players."
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