Ninth-placed Grimshaw was a late addition to the tour lineup, after it was initially reported that only the top eight contestants would appear at the arena shows.
According to The Sun, the 19-year-old has now been informed that he will sign to Syco at the end of the tour if he manages to impress fans during the gigs.
"This record deal is Aiden's to lose," a source said. "If he can keep the fans happy he'll join his mate Matt Cardle as one of Simon's chosen few."
Last week, fellow X Factor competitor Rebecca Ferguson was said to have landed a joint record contract with Syco and Epic Records.