Partey joined the Gunners from Atletico Madrid on transfer deadline-day in a deal worth around £45 million.
The 27-year-old made his full debut for the Gunners in a 2-1 victory against Rapid Wien in the Europa League group stage opener on Thursday.
Partey bossed the game from midfield which earned him the man-of-the-match award.
Arsenal head coach Mikel Arteta hailed the Ghanaian for his performance after the game and another Gunners great Parlour has already compared Partey to Vieira, a player who is considered as one of the club’s best midfielders of all time, and insists the North Londoners have not seen such a strong midfielder in a long time.
Parlour told talkSPORT: “You can see he has got all the attributes to be like a Patrick Vieira. If he gets anywhere near Patrick Vieira we have had the right result as an Arsenal fan!
“They knew what they were buying there – a very strong player that we lacked in that area – but let’s not get carried away, let’s give him a chance.
“Let’s wait until we are playing the big sides like Manchester City, Liverpool, and see if he can boss midfield then. If he can do it then, then we can say we have got a proper player here.”
“He’s a really good presence,” Parlour added. “I don’t think they have had that in midfield. They haven’t been mobile enough over the last few years, but he’s that man to fill in all the gaps.
“He’s six foot one, he’s got that presence, he’s got that mobility in the midfield area.
“When they started flooding people forward trying to get back into the game [against Rapid Vienna], he was the one that just sat in midfield and made everything tick.
“He’s very efficient and had a really good start to his Arsenal career. He could be a really big signing for Arsenal going forward because they have missed someone like him in that midfield area for many years.”