The closing date for applications for the overarching position was Monday, April 11.
Rovers, whose relegation to League Two has been all but confirmed, announced the structural change on April 4 and stated that they hoped to conclude the recruitment process by the following week.
Rovers legend James Coppinger has been linked with the job but neither the club nor Coppinger have commented on the speculation.
Speaking ahead of this weekend’s game against Burton Albion, McSheffrey revealed that an appointment was close.
“I think there’s good progress being made and when the club are ready to annouce it they’ll announce it,” said Rovers’ boss.
“I’m expecting something to be probably announced next week.”
The head of football operations will be tasked with setting the club’s footballing identity and oversee the recruitment, analysis, medical and conditioning departments.
Rovers have had four managers since early last year – Darren Moore, Andy Butler, Richie Wellens and McSheffrey – and hope the new appointment will create more continuity and stability and also help the club bounce back from relegation.