The Hall of Fame pass-catcher and 49ers legend made the suggestion while appearing Monday on 95.7 The Game.
"If you got a player like that, that you can get," Rice said. "That can really add to the offense of the San Francisco 49ers where you let those guys go play, I think you have to go for it."
Rice isn't the only Hall of Fame wide receiver eying a Brown-Bay Area union. Former Dallas Cowboys superstar Michael Irvin told 95.7 The Game last week that it "would be insane" to bring Brown into San Francisco with coach Kyle Shanahan and quarterback Jimmy Garoppolo.
Sources told ESPN that Brown is expected to be traded before the new league year begins in March, when he is due a $2.5 million roster bonus.
Brown has teased fans on social media about joining the 49ers by liking posts and posting a photo of himself wearing a 49ers uniform. He has also communicated with 49ers tight end George Kittle.
Brown, 30, had 1,297 yards and 104 receptions, while leading the league with 15 touchdowns in 15 starts in 2018. He also made his seventh Pro Bowl, but snapped a streak of four consecutive All-Pro nods.
He is under contract through the 2021 season. Trading Brown would cost the Steelers $20.2 million against the 2019 salary cap. Some of that cost would be negated by a $14.5 million cap credit the team receives from Le'Veon Bell's holdout. League sources told ESPN that the team is expected to restructure and extend quarterback Ben Roethlisberger's contract, which would also create more cap room if the team decides to trade Brown.