Coventry have refused to be drawn on whether Iain Dowie is on the shortlist for the vacant manager's position at the Ricoh Arena.
Dowie was sacked in November
Both the former Charlton boss and Macclesfield manager Paul Ince have been linked with the post following the sacking of Micky Adams last month.
"It's down to a shortlist of six, but I will not reveal the names on that list," said City chief Paul Fletcher.
"There are names of managers who are both out of work and with other clubs."
Dowie, 42, has been out of management since November when he was sacked by Charlton after just 15 matches.
Meanwhile, ex-England midfielder Ince took over the reins at Macclesfield in October when they were seven points adrift at the foot of League Two. He has now elevated the club to third from bottom.
There are bound to be rumours about Paul and most jobs because he has done such a good job here
Macclesfield chairman Rob Bickerton
Fletcher is keeping his cards close to his chest because Ince is "employed by another club and he is doing a good job at that club".
He added: "There will always be speculation when a club is looking for a new manager - that is the nature of the business."
Macclesfield chairman Rob Bickerton has insisted it is business as usual for his club.
He said: "Paul and I have talked about it and we are focusing on the next game on Saturday.
"There are bound to be rumours about Paul and most jobs because he has done such a good job here.
"This was bound to crop up but right now there's nothing concrete to say and we are just getting on with it.
"Paul has been quoted as saying his only concern is keeping Macc Town in the Football League."
Coventry sacked manager Adams on 17 January and Adrian Heath was appointed caretaker boss.