The north London club have one foot in the Champions League group stage next season after Arsenal suffered a 2-0 defeat at Newcastle United on Monday night.
A point at Norwich on Sunday will guarantee Spurs a top-four finish and it is likely to mean more funds for Antonio Conte to spend.
The Spurs boss wants to sign six players in the summer and Terrier is one of the players who are on the north London club’s radar ahead of the transfer window.
Talks have already taken place between Tottenham and his representatives and, according to French outlet Foot Mercato, the winger has an offer on his table from Spurs.
The north London club are serious about signing him and have presented the player with a proposal.
Conte is keen on Terrier and wants him to become part of the squad overhaul he is expected to carry out this summer.
But the winger has not made up his mind about leaving Rennes yet and is very much focused on finishing the season at the moment.
The French club are also in line to qualify for the Champions League and a point on the final day this season will also book them a top-four spot in Ligue 1.
