The report claims that Blues legend John Terry will give his ‘seal of approval’ to the move after being impressed by Grealish last season.
Meanwhile, Tottenham boss Mauricio Pochettino has already conceded that there could new no new arrivals at the club this summer.
"Last season I told you some numbers, but this season we don't know," he said this week.
"I don't know if we are going to sign [anyone] or not - we’re working on that.
Chelsea transfer news: Cesc Fabregas begs Eden Hazard to stay
Chelsea transfer news: Can they beat Tottenham to land the Aston Villas star? (Image: GETTY)
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“I cannot tell you if we're going to sign one, zero or two or three or four.
"I think I am working and focused on trying to deliver my job, our job. I try to prepare the team.
"That's the focus and we're concentrating on that."