Mackay interviewed for the role along with former Tottenham manager Tim Sherwood at the weekend and is thought have impressed chairman Steve Parish.
Bookmakers have suspended betting on the Scotsman being chosen by Parish but the only news to emerge from the club was that caretaker boss Keith Millen will take charge of Thursday’s press conference to preview this weekend’s London derby with West Ham.
Millen oversaw last week’s 2-1 defeat to Arsenal, when the Gunners snatched victory through a late Aaron Ramsey goal less than 48 hours after Pulis’ shock departure to heap further misery on Palace fans.
Pulis took charge in November with Palace the heavy favourites to fall out of the division, and led the Eagles on an inspired run which saw them finish 11th.
If he takes charge at Selhurst Park, Mackay will be reunited with Eagles sporting director Iain Moody, who worked with him at Watford and Cardiff.
Mackay was sacked by Cardiff owner Vincent Tan last December, with the team lying in 16th in the Premier League table, and the Bluebirds would later slip to relegation.