The singer, who was linked to the role earlier this week, is said to be the producers' number one choice to replace Simon Cowell when he launches the singing competition in the US.
Bosses have been wooing the 'Not Fair' star for six months and offered her the six-figure deal just before Christmas, the Daily Star Sunday reports. She has also been told that she can miss half the show's auditions to match her schedule.
A source said: "Both Syco (Cowell's company) and ITV are massive Lily Allen fans and the amount of money they're offering her makes it clear they think she will be the biggest draw on the show.
"She's known to have strong opinions and has huge credibility. There was a fear her hectic schedule may interfere with filming, so they've offered to divide the auditions between the judges."
Meanwhile, Louis Walsh is said to be considering a £450,000 offer to return to the panel and Dannii Minogue is "highly likely" to be offered a new deal.