According to him, Rice currently offers exactly what Essien brought to the successful Chelsea side of the mid-2000s.
In comparing the two, Neville said the England man brings power, personality and physicality to the midfield, just like Essien but noted that Roy Keane and Patrick Vieira were in a different class.
"What I think he brings to Arsenal's midfield is power, personality and physicality. Essien brought that to Chelsea,” Neville said on Sky Sports.
“I think that would, for me, be a better example of what I see him as. [Claude] Makelele was the defender, [Frank] Lampard was the goals and then Essien.
"This is not a criticism by the way, Essien was a brilliant player. I loved him at Chelsea. I thought he was outstanding, but he was the power, he was a force for three or four years. I see him more as an Essien. I wouldn't put him personally in the category of Keane and Vieira."
Rice sealed a British record £105 million from West Ham United to Arsenal this summer, although the transfer fee has since been surpassed by Moises Caicedo’s move to Chelsea.
The 24-year-old has since started in each of Arsenal’s Premier League matches this season against Nottingham Forest and Crystal Palace.
The former West Ham captain is yet to score a goal but was voted man of the match in the Gunners’ win over Crystal Palace on Monday.
Rice’s arrival at the Emirates has also seen Thomas Partey shifted to the right-back position in order to accommodate the England international.