Thauvin comes off contract in June and has agreed a lucrative move to Mexico this week.
La Provence says the France international has agreed terms with Monterrey for next season.
But before settling on the deal, Thuavin fielded an offer from Palace - which he refused. It's claimed the Eagles' proposal was the only concrete pre-contract offer received by the midfielder's camp.
Monterrey have offered Thauvin a 5-year deal with a salary of €5m and a significant signing-on bonus.