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.
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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.