The Norwegian joined the Blades from Genk last January in a deal worth around £21.6 million, but has been heavily limited in his game time this season due to a lengthy spell on the sidelines following surgery on a hamstring complaint.
That knock-back has meant that he has played just 13 times in the Premier League this term, and his absence has been keenly felt by a United side who have been embroiled in a relegation battle from the word go.
Gillespie believes that his injury record could put off potential suitors.
He told Football Fancast: “Berge was brought in for a lot of money and he has been injured for most of the season, so that can hinder you because you want somebody with that quality to come in and help the side.
"Berge, who’s going to come in for him? He hasn’t played that much. You don’t know how injury prone he can be, he’s missed a huge chunk of the season.
“I certainly think he would have improved Sheffield United this season.”
Another factor that could inhibit Berge’s likelihood of earning a move away from Bramall Lane is the fact that the Blades are unwilling to lower their valuation of the player.
Heavy hitters like Arsenal and Tottenham are said to be in the race for the 23-year-old, but as things stand, United are determined not to budge on their £35 million asking price.
We’ve gathered the rest of today's Premier League speculation below...