The goalscorer has been a revelation this season and was nominated for the Ligue Une Player of the Year.
Spurs are keen and have tabled a contract offer to Terrier's minders, says Foot Mercato.
Terrier said: "We will see how it goes at the end of the season but I am under contract until 2025.
"I am fulfilled here, I am happy to be here. What is certain is that it is a fantastic season from all points of view because we have a lot of fun and we produce good football.
"We beat our targets in terms of points, number of goals scored. These are good things and it is promising for the future."
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