Former Coventry City player and Manager Micky Adams is favourite for the job although his current bosses at Port Vale are likely to fight any move for their manager.
Sheffield United have issued the following statement: "As the process of preparing the shortlist of candidates is still ongoing John Carver, currently acting in a caretaker role, will remain in charge of team affairs at least until early in the new year.
"The club regards the decision concerning an appointment to be of such crucial importance that it will not be made in haste and will continue to consider the merits of all potential candidates. As a result no further comment will be made until a decision is reached."