Caretaker Chris Morgan, who managed the Blades in their unsuccessful play-off campaign, will be interviewed for the manager's job along with six other applicants.
"Chris has put himself forward to be interviewed for the role," Winter told BBC Radio Sheffield. "We had around 20 applicants of quality for the position and narrowed the shortlist down to about seven.
"We did quite a lot of work in preparing a managerial profile. We want a manager who wants to develop and improve players.
"The manager is pivotal to the challenges we face. It is about creating an identity on and off the pitch, a philosophy and a new culture. The club has to change because it can't continue with the model it has had."
That defeat to Yeovil on Monday meant the Blades are yet to be promoted via the play-offs now in seven attempts and face their third consecutive season in the third tier.