Horne And Corden has been poorly-received in the press, but The Mirror reports that its viewing figures have increased.
A source said: "Mat and James have been completely slated of late, and it's totally undeserved.
"The way they see it, the people having a go at them are middle-aged men with a wife and two kids. This simply isn't their market."
They added: "The BBC has offered them an improved deal but they are reluctant to commit until this series ends.
"Word has got out they're still in negotiations. ITV execs want to get Mat and James on a pay-as-you-go contract.
"It wouldn't be an Ant and Dec-style golden handcuffs deal - they'll be able to pick and choose their projects and still maintain links with the BBC. Mat and James are seen as the future of youth TV."
Horne has returned to the West End production of Entertaining Mr Sloane after he collapsed on stage last week.