The Bluebirds had emerged as favourites to sign the France international last week after the Ligue 1 side announced they had accepted a bid.
|25/1||Cardiff are 25/1 with BetVictor to sign Jordan Rhodes this summer
"Ourselves and Toulouse have come to an agreement," Mackay told reporters.
"We've been in constant dialogue with them in the last week and Toulouse have been excellent to deal with.
"We've got to then have the conversation with Etienne and his advisors. They've been very professional in terms of what they're talking about as well.
"It's pretty delicate at the moment. We're in discussions and negotiations but it's something that's ongoing."
Cardiff were promoted to the Premier League after winning the Championship last season and have already signed Denmark international striker Andreas Cornelius, as well as right-back John Brayford and Brentford goalkeeper Simon Moore.