The Spanish politician and lawyer led Barca from 2003 to 2010.
Laporta was Barca president when Guardiola was promoted from the youth team to senior team manager in 2008.
The contract of the successful coach at Premier League club, Manchester City expires 2021.
“I’m working to introduce myself as a presidential candidate. I’ve been president before and I’m excited to be back,” Laporta said on Catalan station TV3.
“I would very much like Guardiola to come back, but now he is at City and it is a decision that Pep should take. He is a benchmark for Barcelona and many Catalans would like him to coach Barca again.”
During his managerial tenure, Guardiola and the La Liga side won 14 trophies.
Major football competitions remain suspended globally due to the coronavirus pandemic.