He told Chelsea TV: "We would like Frank Lampard to stay at Chelsea for the long-term.
"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."
Inter Milan have not given up hope of taking the player to the San Siro, according to Beppe Baresi - assistant to Inter's former Chelsea boss Jose Mourinho.
But Buck added: "With respect to Inter Milan, the day before yesterday they sent us a latter asking if we would talk to them about Frank Lampard, we responded and said 'no'.
"Yesterday they sent a letter with a cash offer for Frank Lampard and again we responded. We are not interested."