The Barca icon sparked rumours of a return by posting photos of himself at the Camp Nou this week but Laporta has stated that the prospect is fanciful.
Laporta told Catalunya Radio: "His departure wasn't as we wanted. But out of the utmost respect for Messi and everyone at the club, for me to feed speculation that is not realistic is not appropriate."
The president admits that Messi's appearance at the Camp Nou - the first time he has been to Barca's stadium since leaving the club for PSG in 2021 - took him by surprise.
Laporta said: "I didn't know he was coming, but Camp Nou is his home. They told me what happened. It was a nice gesture. He had just finished dinner and felt like coming with some friends. It was a spontaneous act in the spirt of Barcelona.
"It's only fair that Leo should have the most beautiful tribute in the world. When the stadium is finished, we'll have a capacity of 105,000 fans, so we'd like that."
Messi recently lamented the "strange" nature of his Barca exit and was particularly disappointed that he didn't get a chance to bid farewell to the supporters due to the coronavirus pandemic.
The Argentine star told the Barcelona-based publication Sport: "I was left with a strange feeling after I left, because of how everything turned out, because of how I ended up playing my last few years without fans, because of the pandemic. After spending my whole life there, I didn’t leave the way I imagined, the way I dreamed.
"I think the affection of the people will always be there, because of what I said, because of everything we’ve been through."