Lineker had joked back in December that he would present the show "in just my undies" if Leicester City won the Premier League.
Leicester East's Indian-origin MP Keith Vaz asked Cameron if the pundit should keep his promise after the club's triumph.
The prime minister replied that he "absolutely" agreed he should.
Lineker later tweeted: "It seems @David_Cameron is keen to see me in my pants. If that's what does it for you prime minister."
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Bookmakers are now taking bets on what colour pants Lineker will wear, and the 55-year-old has asked if he can place a thousand pounds on polka dots at 33/1.
Vaz was wearing a Leicester scarf in the Commons for the second day running when he asked about Gary Lineker's underwear during Prime Minster's Questions, the BBC reported.
He said: "During this amazing season the local Leicester hero, Gary Lineker, thought the idea of Leicester winning was so farfetched that he said if they did win he would present Match of the Day in his underwear.
Cameron replied: "I absolutely agree. I've been watching everything Gary Lineker has said since.
"He's not quite answering the question, something that of course no one ever gets away with in this house.
"And so I welcome what he said. Obviously I hope it's just the start of him joining the blue team," Cameron said.
Leicester City completed one of the greatest-ever sporting achievements on Monday when the 5,000-1 underdogs won the Premier League for the first time.