Shearer was speaking ahead of Sunday's Merseyside derby between Everton and Liverpool.
He said: “Everton, without doubt, will fancy their chances, as will David Moyes. You can imagine the Everton players and fans looking at Liverpool coming to their new ground on Sunday.
"Everton are flying this season. David Moyes has done a wonderful job, and they've got a chance of qualifying for Europe. They would take great pleasure in beating Liverpool this weekend to help their cause of getting into Europe.”
Shearer, speaking to Betfair, said: “You can imagine how loud the noise will be around (Arne) Slot if Liverpool were to lose on Sunday. I mean, Slot is under pressure anyway. They’ve had a really disappointing season.
"Clearly, he doesn't fancy Mo Salah anymore, because he didn't play him in Liverpool's two biggest games of the season in the Champions League. So, you can imagine mentally what that does to Mo albeit he'll still want to go out on a high. The noise will be really, really loud if Everton beat Liverpool.
“I think, depending on how Everton end the season and depending on how Brentford end the season Moyes has to be in the running for the Premier League manager of the year. I mean, normally, whoever wins the league gets the manager of the year, but David Moyes and Keith Andrews, depending how they finish, will be in with a shout, absolutely.”