The Sunday Mirror says Chelsea will hold Lampard to the final year of his contract rather than sell him - whatever the price.
"Frank is priceless to Chelsea and is not for sale at any price," he said.
"There are further talks planned with Frank and his people and a very lucrative contract offer will be made to him.
"In the unlikely event he decides to turn down a new contract offer we would rather hold him to the final year of his existing deal than entertain the thought of allowing him to join another club."
Chelsea were astonished to hear of reports claiming their 30-year-old midfield kingpin was on the brink of agreeing a £6m-a-year four-year deal with Inter Milan. The insider added: "Talk of him agreeing a deal with Inter - or any other club - is complete and utter rubbish.
"We have not hand any contact with the Italian club or anyone else and interest in Frank is pointless and unwelcome."