Larsson feels that the signing would give every player at the club a boost and increase the competition for places in Gus Poyet's side.
He told reporters: "It would be a really big deal for the club. Fabio was here last year and did really well, so he knows the place and we know him.
"Of course that would be a great signing, but for the people behind the scenes to deal with and we'll have to see if it gets over the line. He showed last year just what a good player he is, especially in the second half of the season.
"We all know what he can bring to the team, and you need as many good players as you can to help improve the competition in the squad. If Fabio returns, it will help everyone else drive on and get better."
Borini scored 10 goals for Sunderland while on loan at the club last season.