O'Driscoll, 53, is among the favourites to become the Blades' third manager this season following Gary Speed's decision to take charge of the Wales national team and Rovers chairman John Ryan has given his local rivals the go ahead to start negotiations.
But Morris told Press Association Sport: "I think, right at this moment, there's a good chance Sean will remain at Doncaster Rovers.
"I'm sure Sheffield United fans and management would call that wishful thinking, but Sean is a big part of what we're trying to build here, he's proud of what we have achieved and we're hopeful he'll want to carry it on.
"There's still a lot more to achieve here and I agree with the comments of our chairman that Blades fans would not necessarily be prepared to give Sean the time he has been given here."
Rovers would demand a big compensation fee should O'Driscoll decide his future lies at Bramall Lane halfway through the season and Morris added: "I should imagine the figure would be substantial. How much is a manager worth if a key player is worth £1million?"
Source: PA
Source: PA