Arsenal and Everton appointed Mikel Arteta and Ancelotti just a day apart after parting ways with Unai Emery and Marco Silva.
The Gunners took much longer to find the right man to take over at the Emirates after sacking Emery in November, while Everton were much quicker in bringing Ancelotti to Goodison Park.
Allardyce was asked why Ancelotti – who is thriving at Everton – didn’t decide to take up the Arsenal job instead.
“I don’t think Arsenal asked him,” Allardyce told TalkSport. “Frightened [to go to Arsenal] because of his reputation and what it might do. Everton, in terms of their spending, are up there with the best over the last couple of years or so.
“Everton are spending huge amounts of money [compared to Arsenal]. Ancelotti, I think would be promised the fact that he could go and sign some of the best younger players. He’s already alluded to that when he’s talking.”