It is understood the Gosport defender has been training with the Blades' development side after West Ham also cast their eye over him.
As reported by The News, Rew was informed last month he would not be handed fresh terms at Fratton Park.
The 18-year-old, who can play either centre-back or left-back, made three appearances in the EFL Trophy.
He also signed pro terms in October 2019 but Pompey have decided not to keep him at PO4 ahead of the 2021-22 season.
Now Rew has gone to Sheffield United hoping to win a deal, having also been watched by Leicester when featuring for the Hammers.
As reported, West Ham ended their interest in Bell.
However, the midfielder has been on trial with Brighton this week while Watford have also shown interest.