The Blades’ 15-goal top-scorer missed the final two games of the season after picking up a calf injury in training ahead of the QPR clash last month.
Sharp’s absence has left United without a recognised senior striker fit and available, although Heckingbottom has said he views Iliman Ndiaye, who has scored in his last three games, as a centre forward.
“Bill’s another few days closer,” Heckingbottom said ahead of Saturday’s first leg at Bramall Lane.
"We’d like him to be (able to play), if he's available to play some part in the tie.
"If he’s not ready, he’s not ready. He is doing all he can and the staff are doing all they can to make sure there is that opportunity.”
Sharp scored 11 goals for Forest during a season-long loan there in the 2012/13 season.
The Blades have no new injury concerns following their 4-0 win over Fulham on the final day of the regular season, Heckingbottom said.
“Morgan (Gibbs-White) has been back on the grass today (Thursday),” said Heckingbottom.
"Conor (Hourihane) and Morgan didn’t train last week.
"We’re fine. George (Baldock) has had more training minutes in him, he’s looking good.
"Touch wood, everything at the minute is as good as it can be.”
Baldock returned to the substitutes bench against the Cottagers having limped off against Bristol City on Easter Monday with a hamstring injury.
Gibbs-White completed 78 minutes on Saturday while Hourihane, who is on loan from Aston Villa, was used off the bench in the final 15 minutes.