Pogba has had a difficult two years since returning to United, with inconsistent form exacerbated by suggestions of a poor relationship with coach Jose Mourinho, whom he has been dropped by on several occasions.
After an impressive World Cup in which he helped France lift the trophy, Pogba emerged as a reported target for LaLiga champion Barca.
The English and Spanish transfer window closed and Pogba remained at Old Trafford, but if Barca are genuinely interested, the rumours will likely persist.
Suarez is convinced the 25 year-old midfielder would be a fine addition.
"He [Pogba] is a part of the elite and has a lot of quality," the Uruguay international said. "I think he would like to compete for more than he is now. He is not a player that belongs to Barca, but quality players would always be welcome."
Pogba's international team-mate Antoine Griezmann was also strongly linked with a move to Barca, but he put an end to speculation just prior to the World Cup.
Suarez acknowledged that Griezmann's decision to stay at Atletico Madrid took him by surprise.
"It was a surprise considering what was spoken about and said," Suarez said. "But everyone has the right to decide and you have to respect their decision. He has earned the respect of the entire football world."