TalkSport pundit Allardyce also claimed that Everton are a 'bigger' club than the Championship side because they have 'bigger ambitions', 'new stadium' on the horizon and 'bigger spending power'.
Everton are currently sitting in the relegation zone in the Premier League, whilst Leeds are hoping to make their long-awaited return from the Championship, as they currently sit in the play-off places.
Speaking to The Alan Brazil Sports Breakfast Show on TalkSport, Allardyce shared his thoughts on Everton, Leeds and their main man in the hot seat.
On Everton fan wanting Bielsa as Everton manager: "They certainly playing what they call attractive football at Leeds," Allardyce told TalkSport. "But they have slipped up in these last couple of years by not getting up. But certainly, he has got a reputation of getting the best out of the players he has got at Leeds United.
On who is a bigger club, Everton or Leeds: "It's very similar, isn't it. You have got the days of Howard Kendall and the days of Don Revie. What would Howard have done [with Everton] if they [England] weren't banned from Europe? What would they have done at Everton? Would they have won the European Cup like Liverpool did? Leeds didn't win it, did they!?
"Everton are bigger because they have got a bigger ambition, they have got a new stadium and bigger spending power and are looking to go places."
Marco Silva is currently under pressure at Goodison Park, and if their poor form continues after the international break then he will be looking over his shoulder.
As for Leeds, it has been a steady start for them, with some top performances, but equally frustrating ones, as Bielsa hopes his team can secure a top-two finish this term.
After the international break, Everton will take on West Ham United on home soil, whilst Leeds play Birmingham.
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