Marco Silva is negotiating with Crystal Palace after travelling to London to discuss becoming their new manager.
Hull City confirmed Silva's departure on Thursday, despite offering the Portuguese the chance to help the Tigers return to the Premier League after their relegation to the Championship.
Allardyce announced his decision to step down on Tuesday, but Palace may have a new manager as soon as Friday with Silva in London for negotiations.
Hull had hoped Silva would stay at the KCOM Stadium, but their vice-chairman indicated that he was likely to leave, telling Sky Sports News that the 39-year-old was "a better calibre of manager than the Championship and wants to manage in the Premier League or at a top European club."
Before moving to the Premier League, the former right-back had managed Estoril and Sporting CP in his native Portugal, and also had a spell at Greek side Olympiakos. He won trophies at all three clubs, leading Estoril to the Segunda Liga title, picking up the Taca de Portugal with Sporting, and winning the Superleague in Greece.
He spent just five months at Hull, winning eight of their 22 games, but could not keep the Tigers in the Premier League.