England midfielder Lampard, 30 on Friday, has 12 months remaining on his current Chelsea contract.
He is expected to hold talks over his future when new coach Luiz
Felipe Scolari takes charge at Stamford Bridge on 1 July.
Reports suggest talks have stalled over the duration of any new deal, with Lampard looking for a four-year extension, while Chelsea are understood to have offered a further two-year deal.
The Italian media believe Inter have offered Lampard a five-year deal, while agent Franco Granello, who claims to be acting on Lampard's behalf, said on Thursday he has a meeting with Inter in 10 days.
Drogba, 30, has also made no secret of his desire to work with his old boss again.
Mourinho indicated when he took over earlier this month that he is looking for up to three players to bolster Inter's Serie A-winning squad.
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