Laporta spent seven years at the helm at Camp Nou from 2003 and Barca went on to win four La Liga titles, the Copa del Rey and the UEFA Champions League twice.
The 52-year-old installed Pep Guardiola as head coach during his tenure, leading to one of the most successful periods in the club's history, winning six trophies in the calendar year of 2009.
"I don't rule it out and the support moves me," he told Esport3. "Each day that passes motivates me more.
"I am not thinking about it, I have work and it doesn't obsess me. It is not my priority.
"In life one must innovate and it is difficult to repeat the past. When the time comes I will make up my mind."
"It [the claims] doesn't surprise me, but it does disappoint me," he added.
"We put together a lot of good players who gave us some tremendous joys.
"I left them the best Barca in history."
