Bracewell won the old First Division and European Cup-Winners’ Cup with Everton.
He told the Liverpool Echo: "The stadium is fantastic. The performance against Chelsea last Saturday was the sort of display and atmosphere that the Evertonians have been looking forward to.
“We’ve been celebrating our great European night, let’s look forward to the next one!
“It’s always a big decision when you move grounds. I’ve been involved with Reidy (Peter Reid) when Sunderland went from Roker Park to the Stadium of Light and Tottenham Hotspur too (he was elite development coach at the academy).
“You need to build a fortress. If Everton can do that and emulate what they did at Goodison Park, then it will be fantastic for both the supporters and the club.
“I was speaking to Reidy, Inchy (Adrian Heath) and the lads who were here and they felt that the win over Chelsea was the first time that they’ve taken the roof off at the new stadium. We all know what this place could be and if they could get into Europe, looking forward to those European nights would be fantastic.
“I worked as assistant manager to David Moyes at Sunderland and then he went to West Ham and won a European trophy. It’s a big ask, but like I say, it would be great come and watch a European night here, and he knows what it takes.”