Bradley, 22 currently has just one year remaining on his Portsmouth deal and his fine form last season has seen a number of clubs take notice - including Sheffield United according to Sky Sports News.
"We are aware that a number of clubs are interested in Sonny and are keeping tabs on his situation," a spokesman for Bradley's agents New Era Global Sports told Sky Sports.
"I am not surprised clubs are keen on Sonny as he was outstanding for Portsmouth last season and if an opportunity comes up that is right for both Sonny and Portsmouth I am sure we will look at it, but he will remain focused and committed to the club until he is told otherwise."
Bradley began his career with Hull City in 2010 but after loan spells at Harrogate Town, Aldershot Town and Swedish side IK Frej the defender was released and in May 2013 he joined the Fratton Park club on a free transfer. The Blades have recently been linked with several defenders with Andy Butler (Walsall), James Bailey (Derby County) and Peter Murphy (Accrington Stanley) all linked with a move to Bramall Lane.