Last weekend, the music mogul lost the first of his four acts in the competition as Jay was sent home from the X Factor during Sunday night's result show.
But, suggesting there is hope yet for Jay in the music business, Simon has revealed he would consider signing the dad-of-one.
Speaking to the Metro, Simon said he believes Jay should use his early exit as an advantage - the same way former X Factor star Ella Henderson has done.
"It's really down to Jay at this point," Simon explained. "I never offer any guarantees... but, we are going to be interested."
Offering advice to those that leave the show week in week out, Simon suggested that Jay, now he is not in the competition, should take the time he has to hit the studio and record demos for labels to hear.
He continued: "Ella was at a similar stage in the competition when she went... She used that pain to make herself more determined. It's down to what [the acts] can deliver themselves."
Simon's comments come after Jay was voted out of the X Factor as the judges' vote was left to deadlock, saving Stevi Ritchie.
Following his exit, Jay told Reveal he felt it was his time to go.
He said: "I actually had an intuition after Saturday night [that I would go] and weirdly I thought it would be me and Stevi in the bottom two... I was a little bit gutted. It meant so much to me."
Hitting back at criticism Stevi should have left instead of him, Jay said he felt Stevie was a better act for The X Factor.
"As a viewer I would have been Stevi all the way," Jay told us. "I'd be like '#BelieveInSteve!' He's so much fun for the show and he's a great performer."
This weekend the remaining seven finalists will take on songs from Whitney Houston and Elton John as they sing again to save their place in the competition.
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Watch Jay perform 'Empire State of Mind II/ New York, New York' here: