The company is transferring its aero engine plant to Inchinnan in Renfrewshire, with East Kilbride set to lose 600 jobs. The move is expected to be completed next year.
And this month Rolls-Royce announced plans to sell its sprawling complex in the Nerston area when it becomes vacant.
Michael McCann, the MP for East Kilbride, Strathaven and Lesmahagow, has written to Rolls-Royce chief executive officer, John Rishton, asking instead for the land to be gifted to the town.
The Labour MP believes profiting from the sale would be a further blow to the town which loyally supported Rolls-Royce for more than 60 years.
He said: "The people of East Kilbride deserve better.
"In my letter to Mr Rishton I reminded him that his company has enjoyed a long and extremely successful partnership with the town.
"So much so, East Kilbride became known as 'a Rolls-Royce town'. I also pointed out that it is my understanding Rolls-Royce received generous incentives to come to East Kilbride when it opened for business in November 1953.
"Consequently, I firmly believe that the company should bequest its site to the people who supported it so strongly since then when that site becomes vacant.
"Doing so would soften the massive blow of losing 600 well-paid jobs. The company's current plan to sell the land and keep the proceeds, should it go ahead, would leave a very bitter taste in the mouth."
A Rolls-Royce spokesman said the firm had invested £85million in the Inchinnan site and hinted that it would use some of the proceeds of selling the Nerston site in further investment in Scotland.
The spokesman added: "We have recently begun the sale process for the site, around 20 months before the planned closure, so that the important regeneration of the site can begin as soon as possible.
"The sale proceeds are part of the justification for our further investment in Scotland.
"It is our firm view that by working together with South Lanarkshire Council and a property developer we can deliver a positive regeneration of the Nerston site without the need for public sector intervention."