The Mirror says the Italian giants say they have reached agreement with Lampard and Chelsea for the midfielder.
It comes just 24 hours after the Blues signed Portugal star Deco, 31, from Barcelona in a £7.9m deal.
Lampard, 30, has been offered a four-year deal worth £24m in total - and the chance to play abroad and link up again with Jose Mourinho at Inter has proved difficult to resist.
Club president Massimo Moratti has yet to announce Lampard's capture publicly.
But privately Inter say the deal is done and that the England star will be unveiled at the San Siro once he returns from holiday in Sicily at the end of this week.