Luis Enrique announced after Wednesday's 6-1 victory over Sporting Gijon that he will step down at the end of the season after three years as the Catalans' head coach.
Ronald Koeman, Mauricio Pochettino and Ernesto Valverde are among those to have since been linked with the position, but Stoichkov believes Sampaoli is the perfect candidate following his successes with Chile and now Sevilla – who sit third in LaLiga and two points behind leaders Barca.
"If the decision were mine, I would like Sampaoli to be Barcelona coach," Stoichkov was quoted as saying by Diario Ole.
"What he did with Chile was not easy, and winning the Copa America [in 2015] the way he did is fantastic.
"If it were down to me, I would appoint him for his winning mentality.
"At the same time, though, it is a decision that has to be thought through carefully."
When asked about the links on Thursday, Sampaoli said he was connected to the Sevilla project "to death".