Cuvelier's father, who also represents him, recently flew over to England to discuss the player's future with Potters director of football John Rudge.
The 19-year-old is highly rated by the Stoke hierarchy and hopes to move closer to Tony Pulis' first-team squad next season.
"His father has been over from Belgium because he wanted to discuss a few things with us and now Flo has agreed a new contract.
"We are just tying up a few loose ends now so he is close to signing.
"Flo is a great lad and one we have been impressed with as a person, as well as a person, in his time with us."
The ex-Portsmouth youngster, who switched to the Britannia two years ago, has yet to make his senior bow for Stoke.
But he enjoyed a productive loan spell at Walsall last season, where he impressed during 18 appearances for the League One side.
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