Cuvelier was brought in for a loan spell at Albion this season before a hamstring injury brought a premature end to his campaign in April.
The Belgian forward’s time in a Brewers shirt was a short but successful one as in his only appearance – which lasted nine minutes – he scored the game’s only goal at Hartlepool.
And manager Hasselbaink is hopeful the 22-year-old can be persuaded to return to the Pirelli Stadium.
Hasselbaink told the Burton Mail: “It’s a big possibility that we could sign him again, if Sheffield United are kind to us.
“We are in the same division, which could be a consideration.
“The group absolutely loves him, he’s really a part of the group.
“He’s part of us, he came to the awards do on Tuesday, he’s one of them who’s slotted in as a human being in the group, but also as a footballer.
“Sometimes the human being side is more important than the footballer for the group.”