Brown posted on his Instagram story Sunday an image of a FaceTime conversation with Rice, who was asked by 95.7 The Game on Monday what was discussed.
Asked by the station if he got the sense Brown would want to play for the 49ers, Rice answered: "Yeah, yeah, yeah, yeah. He wants to come here really bad.
"He's talking about running the hill with me -- doing all that and just working out and just picking my brain. I don't know if it's going to happen because it's going to be up to [coach] Kyle Shanahan and also [general manager] John Lynch, but I'm all for it if they want him to come on board."
Rice, a 49ers star from 1985 to 2000, said he would look forward to passing on knowledge to Brown if San Francisco were to acquire him.
Niners tight end George Kittle had tweeted at Brown after news of his Week 17 drama with the Steelers had surfaced, drawing a response from Brown.
Last week, team president Art Rooney II told the Pittsburgh Post-Gazette that Brown would not be released but "all other options are on the table" regarding his future with the team. He also said that it would be "hard to envision" Brown as part of the team when it reports to training camp in late July.
Brown's absence from Week 17 practices resulted in a benching for the season finale against the Cincinnati Bengals, and during that week Brown had a flare-up in a team setting.
The Steelers would absorb $21.12 million in 2019 dead money on the salary cap by trading Brown, who has notched six consecutive 100-catch seasons -- but taking his $22.165 million cap charge off the books would offset that cost. Brown enters the third year of a five-year, $72.7 million extension signed before the 2017 season.
Rice said he's not worried that Brown wouldn't fit in the 49ers' culture.
"Not a question. No hesitation at all," he said.
Rice said that if he were making the call, he'd definitely trade for Brown.
"If it was left up to me, he'd be here in a heartbeat."
ESPN's Jeremy Fowler contributed to this report.