The Chelsea legend and France World Cup winner came close to leaving Al Ittihad for Paris FC over the summer after their promotion winning campaign.
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Arnault says PFC remain keen to bring Kante back to Ligue 1.
He told L'Equipe: "It's a shame he didn't come; I was disappointed about that. I think he also wanted to move, but his club didn't allow it.
"We respect the decision, but it's a real shame: having N'Golo on the team would have created a significant momentum and perhaps allowed us to gain five more points in the standings."
The president then added that, for now, the interest is no longer current, but Paris FC could return to the midfielder, known for his ball-winning ability and balance in midfield.