Meunier joined Sunderland on a free transfer this summer, having previously said he wanted to stay in France, with the Belgium international suggesting the decision to leave Lille had come from the club's hierarchy.
Speaking before completing his move to the Stadium of Light, Meunier described the outcome as "more the president's decision than mine."
Letang has now offered his version of events in comments carried by French outlet RTL, insisting he remains fond of the 34-year-old but that his wage demands made a new deal impossible within Lille's financial structure.
"I adore Thomas Meunier, and I sent him a quick hello," Letang said. "He said I was the one who decided he shouldn't stay. But if you ask me for four times the club's highest salary..."
The Lille president said he was unwilling to break the club's wage structure, even for a player he wanted to keep.
"What do you think I'm going to say? I'm going to say, 'no, that's not possible.' I'd like to, but I can't. Because I've set a framework for myself, and I don't want to deviate from it."
Meunier spent two seasons back at Lille after returning to the club in 2024, having previously won three Ligue 1 titles with Paris Saint-Germain earlier in his career and represented Belgium at multiple major tournaments, including the 2018 World Cup.
The right-back has since settled into life in the Premier League with Sunderland, joining a squad that includes fellow new arrivals such as Brian Brobbey and Robin Roefs following the club's promotion back to the top flight.
Letang's comments mark the latest twist in what has become a public disagreement between the two parties over the true nature of Meunier's summer departure from the north of France, with each side offering a different account of how talks over a new contract broke down.
Lille finished fourth in Ligue 1 last season, securing Champions League qualification, and Letang has generally been credited with steering the club through a period of financial discipline since taking charge.