The former Three Lions fullback worked with Rice, 27, while he was coaching at West Ham United, and Pearce has revealed that he's keen to see the midfielder take the England captaincy one day.
During an appearance on talkSPORT, Pearce said: "I've always viewed Rice from afar ... maybe I'm slightly biased towards him as I've worked with him ... that he'd thrive in an environment like that.
"I would love to see him as the Arsenal captain, I can't believe that he's not Arsenal captain.
"I think he would flourish in the role and he is captain material, so him being England vice-captain is fantastic to see."
Harry Kane is the current England captain, but Pearce wouldn't be opposed to Rice succeeding him in the near future.
He said: "That's the hope I think, his esteem will rise on the back of that. Kane is the captain, but there's a little bit of me that would love to see Declan as the captain, with Harry in the team."
Pearce has also downplayed suggestions that Jude Bellingham might feel disgruntled to have been overlooked for the vice-captaincy.
The former England international stressed that Bellingham, 22, needs to secure his place in the England team first, before he aspires to become the skipper.
Pearce - who famously missed a penalty during the 1990 World Cup semi-final against West Germany - said: "He's got to get in the team first [to be upset].
"The fact that he's picked Rice and the timing of it, I'm not sure whether there's something there that Bellingham captained the team the other day [against New Zealand], but whatever."
Pearce urged Bellingham to focus on his own performance first and help England to win their first World Cup since 1966.
He said: "Listen, he's done brilliantly, 40 caps at the age he's at, he's going to be one of the all-time cap-holders and hopefully he'll have a winner's medal to show for it as well."