The Blades go into their final three matches sitting fourth in the table, five points adrift of second-placed Bournemouth, with a game in hand on Eddie Howe's side.
Morgan, who replaced Danny Wilson as boss at Bramall Lane last week, believes that his side can still finish in the top two.
"We've got three games remaining and I think we'll be sitting in the dressing room before the Preston game knowing a win will give us a chance of automatic promotion," Morgan told Sky Sports News.
"I might be proved wrong, but I'm optimistic we can take the race to the final day of the season.
"The top two remains in our sights and the results in the next week or so are going to have plenty of twists and turns, I'm sure of that."
Sheffield United play Portsmouth on Saturday afternoon.