According to BBC football correspondent Jonathan Legard, Chelsea still expect Lampard to see out the final year of his contract and, if anything, sign a new longer-term deal, but Inter remain confident.
"They believe they will still get their man, but think it will take longer than they initially thought," Legard explained.
"They originally thought they might be able to strike a deal within a matter of days. But despite Chelsea's denials that any fax from Inter has arrived or that negotiations have started, Inter believe they are underway.
"They are also looking at Ricardo Quaresma at Porto and Mancini at Roma and they hope that when Jose Mourinho unveils his squad on 16 July, Frank Lampard will be there in an Inter shirt."
Lampard met new Chelsea boss Luiz Felipe Scolari on Monday as the Chelsea squad returned to their Cobham base for pre-season training.
Scolari may shed some light on the situation on Tuesday when he addresses the English media for the first time.
He is also likely to face questions about the future of Chelsea striker Didier Drogba, who has also been linked with a move to Inter.
Mourinho indicated in June that he would like to work with the Ivory Coast international again.
"I cannot forget Deco, Lampard and Drogba. These are players who I could never say no to," stated Mourinho.
"I would love to work with them again in the future but I don't know which of these three will leave their clubs, but we will see."
If Mourinho bids for Drogba then he may face a fight for his signature from city rivals AC Milan, whose technical director Leonardo told BBC Sport that they are also keen on the forward.
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