There has been speculation over the futures of Ronaldo, Edinson Cavani, and Marcus Rashford, and the Red Devils have been looking for alternatives to bolster their forward line.
Firmino is out of contract at Anfield next year and found himself in and out of Jurgen Klopp's side this season, and former United midfielder Kleberson believes the Brazilian will fit in perfectly at Old Tafford.
"Roberto Firmino's style would suit Manchester United, especially the way he plays for Liverpool," Kleberson said.
"For the Brazil national team, he plays higher up, but for Liverpool he's a bit deeper. If Manchester United wanted to make a change, he's a good player that can help, especially with Marcus Rashford and Jadon Sancho on the wings. Firmino can help those players create space when they're on the attack.
"That's the type of player Manchester United should be looking at. A player with Firmino's quality can help release the team. He's a great player and he'd be a good fit, and a good signing for Manchester United."
Firmino has scored nine goals for Liverpool this season but has falling down the pecking order in favour of Diogo Jota and Lucas Diaz.
United have struggled this season in front goal, depending majorly on Ronaldo to provide goals. The Red Devils find themselves battling to finish fourth in the Premier League and were knocked out of the Champions League by Atletico Madrid in the last-16 last week.