The 48-year-old believes that Aston Villa can build a team around the England international.
Grealish is currently the Villans talisman, having been their best player since their return to the English top flight.
Despite being out with injury at some point last season, he scored six goals and provided 12 assists in 26 Premier League games.
Manchester City are said to be yearning to sign Grealish this summer for a fee around £100million, which will make the 25-year-old the most expensive player in the Premier League history.
Parlour has told Grealish not to be tempted with the Premier League champions’ offer.
Parlour said on Friday’s talkSPORT Breakfast: “I really hope he can stay. It would be so great if Grealish came out and said, ‘No – I’m staying at Villa, this is my club’.
“Hopefully the owners say, ‘Let’s build a team around Jack, let’s get one or two players in and really have a go’.
“They could be a huge club, they are a big club anyway, but they could try and break into that top six or even top four.”
Meanwhile, former Manchester City winger Trevor Sinclair agrees that Grealish won’t be in a rush to leave Villa Park.
He said: “Villa are going forward and they’re ambitious, I don’t think Jack will be desperate to leave.
“He loves the club, he’s shown that loyalty, so I think City will have to pay top money for him because Jack won’t put in a transfer request, he’s not going to ruffle any feathers.
“I think £100m is a bit steep, but if you knock on someone’s door, ask to buy their house and it’s not for sale – you’ll have to pay a premium!
“That’s the case with Grealish. He’s happy at the club and he’s loved by the fans.”
