For some time last season it appeared Chelsea were prepared to allow Lampard's contract to expire, before the club's record goalscorer agreed a one-year extension.
"I told him when I was not Chelsea manager and he didn't have a new contract, just by being a friend, I told him that I didn't see him playing for another English club and I wouldn't see him play in another small league, because of his nature," former Real Madrid boss Mourinho said.
"He demands a lot from himself. He wants to play at this level and I think he can."
Mourinho insists the use of the 35-year-old Lampard must now be managed, though.
"He is not 25 anymore, so the crazy Lamps that wants to play every minute of a Carling Cup match against a team from the Championship, the crazy Frank that wants to play and beat the record of appearances and play every minute every match is not here anymore," Mourinho said.
"Now it's about to keep his performance high for the most time we can, for the most seasons we can."
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