Cuvelier, formerly of Stoke, joined the Blades from the Potters for an undisclosed fee in September but the 21-year-old has made just two appearances since Nigel Clough became the manager at Bramall Lane the following month.
"We all saw his ability when he was at Walsall and that's when he first came on the radar, not necessarily when he played for Stoke reserves, but certainly at Walsall he had an impact on them," Vale boss Micky Adams told the club's official website.
"He has got good ability and he can handle the ball, but has got to get himself in the side first of all. He is up for the challenge and he wants to do well.
"He has had very little football at Sheffield United so if there is one worry it is that. He might need four or five games to get himself up to full speed.
"We can't afford four or five games, we need him to hit the ground running if he possibly can, but until he plays we won't know."
Cuvelier will be available for selection for Saturday's home game against Oldham. He will also be eligible for Vale's fourth round FA Cup tie against Brighton next weekend.
Meanwhile, Adams revealed he is looking to add a couple more new faces to his squad during the transfer window, but they will be players with limited experience.
He added: "We would like to add another couple to supplement the squad and I have to say they will probably be youngsters out of a Premier League side, so people with very little experience in the Football League and who are reasonably cheap."