The Blades have confirmed they have received one offer from Crystal Palace for the 23-year-old, who was reportedly being monitored by Reading during their FA Cup win over Danny Wilson's side at the Madejski Stadium on Saturday.
Blades chairman Kevin McCabe told BBC Radio Sheffield that a decision on Blackman's future would be decided this week, with Thursday's transfer deadline set to force the issue.
"We have had a bid for Nick, but he played (on Saturday) and is still very much our player as we speak," Wilson said after the 4-0 defeat at Reading.
"I would like him to stay for sure, he's a very good player and our leading goalscorer."
Blackman has scored 14 goals in 33 appearances for the Blades this season since signing from Blackburn for an undisclosed fee in the summer.
United have slipped out of the automatic promotion places in recent weeks after failing to win any of their last four league games and Wilson is hoping to strengthen his squad.
"We would be foolish not to be worried about recent results," he added. "But this was something of a one-off and hopefully we will have players returning to fitness in the next week or so in addition to hopefully a couple of further signings."