Former Middlesbrough, Sheffield Wednesday, Sheffield United and Bradford City defender McMahon oversaw Saturday's 4-1 defeat at Ebsfleet United, following the sacking of his previous boss, Mikey Morton, as manager.
The 37-year-old has made it clear he does not want the job in the long run.
But the Conference club say plenty of others do, so in an update to supporters they have stressed they will not be rushing into an appointment.
The Minstermen have new owners this season, an last week brought former player Darren Kelly back to the club as general manger.
"The managerial process will be led by the recruitment team," they said in a statement. "The York City recruitment team have a clear blueprint when identifying suitable candidates who are a good fit for the football club.
"The recruitment team have gone through all applications, spoken to many managers and agents, and will now take the necessary time to assess, identify and then meet candidates to present at interview.
"Given the size, supporter base and potential of the club, the role is attracting a lot of interest and it is very important that the club takes the appropriate time in making a selection given the importance of the role.
"This is an attractive role within a hugely ambitious football club and we want to ensure we leave no stone unturned in looking for the next manager.
"York City have ambitious owners who want to see a football team on the pitch that the supporters will be proud off. It is important that we undertake the appropriate due diligence to ensure that the selection process arrives at correct decision in a timely manner."
Former Halifax Town and Scarborough Athletic manager Kelly – he also played for the latter – has held sporting director roles at Newport County and Hartlepool United.
York's next game is at home to Boreham Wood in the Conference on Saturday.
The only team below them in the table are Southend United. They have won four of their opening seven matches, but are a point adrift because of a 10-point deduction for financial issues.