The Blades have been relegated to the Championship at the first time of asking.
However, The Telegraph states that Aston Villa are among the teams chasing his signature.
Arblaster, who is only 20, is wanted by West Ham United as well, while other teams are likely to come into the mix.
Sheffield United now face a battle to keep the England Under-20 international.
Arblaster may not fancy a season in the second division, but manager Chris Wilder hopes to convince him to stay.