Both Everton and West Ham are being linked with a move for former Brighton and Chelsea manager Potter who will have a tough choice between the two sides in the coming weeks.
Potter is said to be top of the list to replace Hammers head coach Julen Lopetegui, who is on the cusp of being sacked with Saturday's 4-1 defeat at Manchester City increasingly looking like his final game in charge of the club.
Everton however have recently confirmed their takeover by The Friedkin Group which could put manager Sean Dyche under pressure as he leads his side against a relegation battle once again this season.
Carragher spoke to Sky Sports as he weighed up the English coach's options and what club he thinks Potter is more likely to go for if the opportunity arises
“In my head, I think Everton are a bigger club than West Ham,” he told Sky Sports.
That’s maybe me going back to my childhood and watching Everton win trophies and West Ham not really winning too much.
“But Everton have been so poor for the last ten years. West Ham have won a European trophy, they’re in London, they’ve got the Olympic Stadium. Everton have got the stadium coming..
“I do think that is more of a 50/50 decision. Maybe right now, you’d probably veer more towards West Ham because they’re probably guaranteed to stay in the Premier League next season. So I think he’d probably go for West Ham.”
“It’s probably sad really that I’m saying that’s a 50/50 decision because in my mind, Everton are a much bigger club than West Ham.”