"As is his right, he has decided at the moment not to accept that contract - but there is one year remaining on his current contract and we expect and hope he will honour that contract.
"Even for the course of that year there is still the opportunity for him to complete a new contract because the offer we have made him remains on the table."
New coach Luiz Felipe Scolari insisted Lampard was happy to stay, but his agent, Steve Kutner, said the player's future was "completely unresolved".
Scolari revealed on Tuesday that Lampard had told him he wanted to stay "for more than one year".
"I was very happy because I asked if he wants to stay and he said 'yes, I will stay at Chelsea'," said Scolari.
However, Kutner's response soon after Scolari's news conference cast more doubt on the player's future.
Talks over a new deal for Lampard have been on-going for two years without success, and Chelsea face the prospect of the England international leaving for free next summer if the matter is not resolved.
Scolari wants a "family" atmosphere in the squad
"You've got Inter claiming they've made a bid, Chelsea saying that they are not entering into discussions over a transfer and Lampard pretty much saying meet my terms," said BBC football correspondent Jonathan Legard.
"The Lampard team are not happy, they are frustrated. Lampard wants to stay - exactly as Scolari said in his press conference - but he would like a five-year deal and Chelsea are only offering four on, from what I gather, about £150,000-a-week.
"If Lampard feels that Chelsea won't meet his terms then perhaps he needs to look elsewhere and that is why Inter have come back again and are still confident they can get him to play for them next season under Jose Mourinho."
BBC 5 Live also reports that Chelsea insist there was no row between Lampard and chief executive Peter Kenyon at the Cobham training ground on Tuesday, despite reports to the contrary.
And at his first news conference in England since taking charge, Scolari insisted he envisaged Lampard's long-term future being in south-west London.
"I met him on Monday and told him that I like him very much as a player and as a person and I asked him if he wanted to stay, not only for this season but for longer," added Scolari.
"After we had spoken for 15 minutes, he said he wants to stay and play for Chelsea for many years.
"I am very happy because I think Chelsea need Lampard and I think he is with us for more than one year."
BBC Sport revealed on Monday that Inter had contacted the Blues over Lampard.
There was an offer and we confirm it
Inter Milan president Massimo Moratti
However, a statement on Chelsea's website on Tuesday read: "We have informed Inter that we will not enter into any discussions regarding the transfer."
Despite Chelsea's insistence that they had not received an offer from Inter, the Italian club's president Massimo Moratti claims a bid was made.
"This is not true," said Moratti. "There was an offer and we confirm it. However, we don't want to create any big problems.
"They replied that they have no intention of negotiating, as was their right. Now we will see."
Lampard also has an option under Fifa rules to buy out the remaining 12 months of his contract.
Scolari has already signed Portugal midfielder Deco from Barcelona to join the Blues' already considerable midfield resources.
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.