Butt took the job from fellow co-owner Gary Neville in 2022, but feels he can no longer give the position the time it deserves.
The League Two club have stalled in their progress over the past 12 to 24 months.
"Whilst I have enjoyed the day-to-day responsibilities of the chief executive role and discovered a huge amount about the challenges an EFL club faces away from the football pitch, I have recently realised how much I miss the coaching and development of players, and this has increased my desire to get back into that side of the game," he said.
"Over the past few months there have been several exciting opportunities put forward to me that have put my focus back on coaching and on the grass.
"That being said I have always wanted to put Salford first, and we now have experienced executives within the senior management team here which means that I can step away from my current duties without any impact on current operations and it will be very much business as usual."