Mackay was expected to succeed Tony Pulis at Selhurst Park before his former club Cardiff sent a dossier to the Football Association detailing allegations about his time in Wales.
The allegations also involve Iain Moody, Palace's current sporting director who worked alongside Mackay at Cardiff, and the FA has confirmed it has opened an investigation into the matter.
Sky sources say Moody's position at Palace is now untenable, and he is likely to leave the club later on Thursday, while Mackay is now out of the running to be manager.
Another candidate, Glenn Hoddle, has ruled himself out and will instead concentrate on his media work and his role assisting Harry Redknapp at QPR.
And that leaves former Tottenham boss Sherwood as the clear favourite with Sky Bet ahead of Steve Clarke and Martin Jol.
In the meantime, Palace's caretaker boss Keith Millen is due to face the media after 2pm on Thursday ahead of this weekend's home game against West Ham, and you can see what he has to say on Sky Sports News HQ.