The Parkhead club's hopes of enticing Henrik Larsson to give up his job at Falkenberg in Sweden and return to Paradise appear to be fading.
And this has moved former Hoops defender Mackay (left) and life-long supporter Coyle up the wanted list.
Chief executive Peter Lawwell continues to insist that the club will take its time in making the appointment.
However, behind the scenes, potential candidates - identified even before Lennon publicly announced his departure on Thursday - are being sounded out to establish who would wish to be considered for the position.
Roy Keane's willingness to be included in the shortlist appears to have taken on a more positive hue over the past couple of days.
And there is no doubt the man currently working in a part-time capacity as assistant manager to Martin O'Neill with the Republic of Ireland national team - Scotland's Euro 2016 opponents lost 2-1 in a friendly against Turkey at the Aviva Stadium last night - would represent a high-profile appointment.
However, since the news broke that Lennon was leaving, there have been several other notes of interest delivered to Celtic.
And major shareholder Dermot Desmond and Lawwell will carefully assess them all before they make their move for the man they believe can continue the successful work carried out by Lennon over the past four years.
Former Cardiff and Watford boss Mackay along with former Burnley, Bolton and Wigan manager Coyle - the choice of Desmond to succeed Gordon Strachan in 2009, but who declined the offer to stay with newly-promoted Burnley - both have the advantage of being available to start work immediately and without compensation, as they are currently free agents.
With the transfer window due to open at the start of next week, and the squad set to report back in less than a month to prepare for their opening Champions League qualifier on July 15 or 16, the club would benefit greatly from a speedy conclusion to the process of apppointing a new manager and backroom team, as coach Garry Parker has joined assistant manager Johan Mjallby in calling time on his career at Parkhead.
There are also players whose contracts need to be addressed, including this season's top scorer and Scotland's Player of the Year, Kris Commons.
The 30-year-old is about to enter the 12-month option period of his current deal.
And though the attacking midfielder has said he would like to extend his stay at Parkhead, and Lennon was adamant he should be retained for at least another two years, discussions over the terms of a new contract have yet to begin.