Neymar left Barca for PSG in a world-record €222million transfer in 2017, but the Brazilian forward continues to be linked with a return to Camp Nou.
The 28-year-old failed to make his way back to LaLiga champions Barca at the start of the 2019-20 season and he is reportedly a transfer target again.
Rosell was president when Barca signed Neymar from Santos in 2013 and the 56-year-old heaped praise on the Brazil international.
"If I were the president of Barca, I would try to sign Neymar," Rosell told COPE and Radio Marca.
"He is the second-best player in the world after Messi and fits perfectly into the philosophy of the club.
"But with experience, he would sign him with two contracts, one sports and the other behavioural."
Since swapping Barca for PSG, Neymar has won three successive Ligue 1 titles, to go with Coupe de France, Coupe de la Ligue and Trophee des Champions honours.
Neymar scored 13 league goals before Ligue 1 was suspended due to the coronavirus pandemic and PSG were eventually declared champions.
Barca, meanwhile, have been tipped to sign Inter star Lautaro Martinez in the off-season.
However, Inter have insisted Martinez will not be sold unless his release clause – reportedly worth €111m – is met.
Rosell added: "I would not sign Lautaro for €111million but I would try to exchange two players".