Murphy is on a three-man shortlist along with Derby County's Johnny Russell and Watford's Daniel Pudil.
Scottish forward Murphy was a real threat for the Blades last season, scoring 12 goals and providing 12 assists in all competitions, and awarded the club's joint player of the season honour along with Chris Basham.
Murphy extended his contract with the League One side in January, with it currently standing to take him until 2017 as per The BBC, placing Sheffield United in a comfortable negotiating position for a player they are not expected to want to lose.
Why Leeds United could be affected by Brighton's transfer plans
Sheffield United have been strongly linked with a deal for Leeds United's Billy Sharp.
Newspaper the Sheffield Star reported last week that Sharp is wanted by manager Nigel Adkins, who bossed Sharp at Scunthorpe, Southampton and Reading.
Sharp is an out and out striker while Murphy is more versatile, often played out on the wing, but his goal return of 12 is not one many wide players can easily replace.
It would take a sizeable offer from Brighton to convince the Blades to sell Murphy - yet they may need this themselves to prise Sharp away from Leeds.
Sharp can be a 20-goal a season man in League One, a player who can make a significant impact in helping them finally achieve promotion after numerous play-off near misses.
If it comes down to Murphy or Sharp, and the will of both players is to make the move, Sheffield United could have to make a big decision.