Allardyce was the bookies' favourite at one time to succeed Ronald Koeman on a permanent basis and was reported to have spoken with Farhad Moshiri about the position — something he initially denied — but any offer for his services is believed to have involved a short-term contract.
The former England manager was on the radio again this morning to discuss his links with the Goodison Park hot-seat and he explained that he didn't feel as though the club wanted him badly enough.
"It never materialised as I thought it would, unfortunately," Allardyce told talkSPORT. "For me such a long time without a decision [meant] I had to make a decision myself.
"The decision was it was probably better it wasn't me, and I'd move on to something else. It would have been a fabulous job, but it just didn't feel right.
"I think when you're sat in my position you want people to be decisive and feel like they want you. I didn't get that feeling overall. They were hesitating that I was the man."
Everton have made overtures to Watford for their manager, Marco Silva, but have been told that no talks will be permitted with the Portuguese who has only been at Vicarage Road for a few months.