© Rex Features / David Fisher
Last weekend, it emerged that the programme's current hosts Adrian Chiles and Christine Bleakley will be axed from the series shortly.
Williams currently works on the BBC's rival morning show Breakfast, but reports have now claimed that she has been approached for Daybreak.
The rumours have been fuelled by previous reports that Williams does not want to move to Salford when BBC Breakfast relocates.
"ITV want someone who is equally at home grilling major figures as well as handling the more trivial topics that light up early morning viewing," a source told the Daily Mail.
"They believe they may be able to tempt her to join them because her life revolves around London."
Meanwhile, an alleged insider told The Sun: "If ITV managed to lure her away, it would be a huge coup."
However, a spokesperson for ITV denied the reports, while representatives for Williams and BBC Breakfast declined to comment.
When news of the Daybreak shakeup first leaked, Natasha Kaplinsky and Eamonn Holmes were named as frontrunners for the show.
Holmes has since confessed that he would like to be considered for the job but Kaplinsky appears to have ruled out the possibility.
> Adrian Chiles confirms Daybreak axe: "We didn't want to go"
