Caretaker manager Paul Warne has been in charge of the Millers since Kenny Jackett's departure on 28 November.
"Paul Warne, Matt Hamshaw and John Breckin will remain in control of the first team throughout the Christmas period," said a club statement.
"The club will continue to work towards a position where we can announce a more permanent solution in early January."
Rotherham, who are bottom of the table and have lost 13 of their past 15 matches, host 23rd-placed Wigan on Boxing Day and 21st-placed Burton three days later.
The statement added: "Paul Warne and his staff will work closely with our new head of recruitment Jamie Johnson to indentify, and move for, targets ahead of the upcoming January transfer window."
Warne has said that he does not want the job on a full-time basis.
Former Wolverhampton Wanderers boss Jackett was in charge of the Millers for 39 days before offering his resignation.
Rotherham have had five permanent managers and three caretakers since the start of last season, with Neil Redfearn, Neil Warnock, Alan Stubbs and Jackett all having spells in the job following Steve Evans' departure in September 2015.
Eric Black was placed in temporary charge after Evans left, while Nicky Eaden was appointed caretaker-manager when Redfearn was sacked in February - although Warnock was appointed before the former Birmingham and Wigan defender had the chance to lead the team in a game.

Bosses at the Brimmond Medical Group practice in Bucksburn said a lack of trained GPs, diminished resourcing and extra demand from new housing developments had left the business "unviable".
The group's Dyce surgery has more than 8,000 patients.
Responsibility for primary care will be handed to NHS Grampian from October.
A letter to patients stated that there had been "progressive problems with GP recruitment and retention".
It read: "Inevitable staff turnover has become impossible to manage in the context of an inadequate number of trained GPs being produced, and a collapse in those GPs seeking partnerships in GP businesses.
"Brimmond Medical Group is faced with a number of GPs leaving or retiring - and an inability to adequately replace them.
"Locally, combined with substantial extra expectation from new housing developments and massively diminishing resourcing, the business of the practice has become unviable."
The British Medical Association has warned of a crisis in GP staffing due to the number of doctors planning to retire or move abroad.
However, the Scottish government said recent investment in primary care had seen the number of GPs increase by almost 7%.
Championship strugglers Rotherham United aim to name a permanent first-team boss in "early January".
[NEXT_CONCEPT]
An Aberdeen medical practice is to be dissolved, in part due to a shortage of doctors.