The Catalan club are determined to add a right-back to the squad having failed to replace Dani Alves following the Brazilian's move to Juventus last year, with Bellerin their main target.
Bellerin progressed through prestigious Barca academy La Masia before opting to join the Arsenal academy in 2011.
After three full seasons with the first team, however, reports linking him with a return to Camp Nou have intensified and Arsenal's failure to qualify for the Champions League next season is reported to be the deciding factor.
With Arsene Wenger rebuilding his squad ahead of the 2017-18 Premier League campaign, Bellerin is rumoured to have the option to leave for La Liga, and midfielder Suarez believes his international colleague is keen on a move.
"I have spoken to Bellerin but it is not an easy situation because Arsenal trusted in him since he was a boy," Suarez told TV3. "It is his decision, and Arsenal's decision. I really don't know what is going to happen but I wish he can come.
"Both Sergi Roberto and Aleix Vidal have had amazing seasons in that role but if, finally, Bellerin is coming he would challenge with them to be picked in the starting line-up, but Bellerin and Roberto can play in other roles; it is not easy replacing the best right-back ever.
"I have spoken to him [Bellerin] and from one side he wants to join Barca, but from the other he feels very attached to Arsenal. It is a hard situation and I am nobody to be speaking about this, but I wish he can come."
Bellerin, who is currently on international duty with Spain at the Under-21 European Championship in Poland, is said to be hoping his representatives push through a move while he is away.
Alongside Bellerin and Suarez in Poland is Gerard Deulofeu, another player linked with a return to Barca.
Asked about details of Deulofeu's future, Suarez said: "He himself is not even clear what will happen this summer."