Former Cardiff City and Wigan boss now linked with Celtic job.
Neil Lennon, the Norwegian's predecessor, told BBC Scotland this week he would be keen to return when Deila leaves at the end of the season.
Now Mackay, sacked by Wigan Athletic a year ago, has declared his interest.
"If Celtic wanted to talk to me, I'd certainly be keen to do that," the 44-year-old told Sky Sports News.
Former Watford and Cardiff City boss Mackay was subject to a Football Association investigation after leaving the Welsh club, when it emerged that he sent text messages containing discriminatory language.
However, the FA confirmed last year that no disciplinary action would be taken, highlighting "serious concerns about the circumstances in which particular evidence had been given and the reliability and completeness of that evidence".
Mackay recently told BBC Scotland that he wished for a quick return to club management and that Celtic was a "huge, worldwide job".
"I think the next five-year period at Celtic is a crucial one," Mackay said. "I think a record 10 titles in a row is achievable and a strong focus should be there.
"But, for that to happen, I think there is a detailed and strategic plan needed going forward. I think I could help with that and bring a fresh approach.
"I've got an understanding of the club and an ability for that to happen."
Mackay was speaking after Deila announced last week that he would stand down in the summer.