Messi, 35, spent 20 years at Barca and helped the club win 35 trophies but left for Paris Saint-Germain in August 2021 because of a financial crisis at Spotify Camp Nou.
There has been speculation that Messi, who becomes a free agent in June, will consider a return to Barca.
"He [Messi] has the doors of Barca open," Laporta told the Joe Pomp show. "He knows that. He's part of our emblem.
"Messi is a player of PSG and I have to be careful what I say. I have to respect his club and respect him. Messi knows that we have Messi in our heart, Messi is part of our blood.
"I need to find a way to improve this relationship between Messi and FC Barcelona. We will see. Right now he is a PSG player."
Messi famously cried at his his farewell press conference but an indication that his relationship with his former team has deteriorated surfaced last month when his brother, Matias, took a swipe at Barca and Laporta.
Matias later apologised for his comments.
At the time of Messi's exit, Laporta called the decision the "hardest he ever made" but said "he did not regret it because the club always comes first."
Laporta continues to defend his decision.
"When I arrived for a second spell [as president], the legacy that we inherited wasn't very good and I had to take a decision that I'm not satisfied," Laporta added on the Joe Pomp show. "I'm sad because of this.
"Messi is the best player in the history, he played at our academy, he is the most important player in the history of FC Barcelona."
The PSG forward received a powerrful ovation from the 83,000 crowd at the Monumental stadium.
The French giants signed Messi in the hope that he would lead them to their first Champions League title but it has not happened, with the club bowing out this season in the round of 16 to Bayern Munich.
Messi has not spoken about his future.
"He is going through a great moment because Argentina won the World Cup," Laporta said of Messi. "We were pulling for Argentina to win. We wanted Messi to be recognised and win the World Cup. We are very happy he did."