The full-back has long been linked with a Camp Nou return although Barca are also reportedly interested in signing Benfica’s Nelson Semedo.
Bellerin recently appeared to play down talk of a move to Camp Nou by tweeting "Don’t believe everything you read" apparently in response to the speculation.
However, Suarez is hopeful Bellerin will move back to Spain in quotes that are not likely to impress Arsenal manager Arsene Wenger.
"I have spoken with him, and on the one hand he's keen to come and on the other he feels tied to Arsenal -- I hope he can come," he told Catalunya Radio.
Suarez also spoke out about Gerard Deulofeu who has also been tipped to head to Barca this summer with the club having a buy-back option, adding "he himself is still not clear what will happen."
It seems clear that Barca are keen to bring Bellerin back but he will not come cheap and convincing the player and Arsenal, looks a tough task at present.