The bid from PSG arrived just as the now 18 year-old was breaking through into then coach Xavi's first team.
Speaking today on Cadena SER, Laporta said: "We had a formal offer of 250 million (euros) for Lamine, through his agent and confirmed with people from PSG.
"At the time they came, explained it to us face to face and we said no, it was a time when Barça was in great difficulty."
With centre-forward Robert Lewandowski coming off contract this season, Laporta was also about renewing the 37 year-old's deal.
He said, "First, because he's a very talented player, a goalscorer, and always on fire when he comes on. And then because there's another very clear point: if he wants to stay, I've always given great players another year on their contract as a token of appreciation.
"I'm very grateful to Lewandowski because it wasn't easy to come to Barça, and he said, 'Because of my quality and my track record at Bayern, I want to play for Barça now because I've always wanted to, and you have to let me go.'
"He gave up a lot to come to Barça, and that's why I'm so grateful to him."