According to the Daily Mirror, ITV is prepared to offer Ross £15m over three years to bring his chat show to the channel, with Channel 4, where he first found fame in the 1980s with his show 'The Last Resort', prepared to match that sum.
If he agrees to a move it will not be until after next July, when his current BBC contract comes to an end. It is understood that the BBC has already offered Ross a £12.5m three-year deal, which he is also considering.
Even if Ross accepts the reportedly lower BBC offer, it would still make him the UK's highest-paid TV presenter to date.
It would also eclipse chatshow host Paul O'Grady's move from ITV to Channel 4 in a £3m deal earlier this year.
If Ross were to leave, it would come as a massive blow to the BBC because he has become one of its most popular stars across TV and radio.
The corporation has failed to match his success with its other big-name signings, such as Graham Norton and Davina McCall, who have fronted a string of flops and critically panned shows.
As well as Ross's chatshow, he also presents 'Film 2006' and 'Hollywood Greats' on BBC One, and the Saturday morning show on BBC Radio 2.
In a leak to the press last week, it emerged that Ross receives around £530,000 for the show, which equates to £60 a minute. The BBC has now launched an inquiry into the leak, which also revealed the salary details of a raft of other DJs.
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