Everton are reportedly considering changes this summer.
Allardyce's style of football isn't resonating with Everton fans right now, whilst two wins in the last 10 games in all competitions mean that form isn't quite finding the Toffees right now.
With Allardyce's contract only until the summer of 2019, Everton could yet make another change this summer, and the Daily Mail believe that Shakhtar's Paulo Fonseca – a target around the same time as Allardyce – could be a target again.
Add in that director of football Steve Walsh is also under pressure after a host of expensive flop signings, meaning a move for PSV Eindhoven's Marcel Brands could be on the cards, and majority shareholder Farhad Moshiri may be planning an exciting double move.
Fonseca dominated Ukrainian football last season with a domestic treble, whilst he also took his side into the last 16 of the Champions League this season, with a two-legged tie against Roma to come.
The Portuguese boss has played an expansive 4-2-3-1 system with Shakhtar, relying on the creative talents of Brazilian-born trio Taison, Marlos and Bernard to cause mayhem, whilst another Brazilian – Fred – has been the energy in midfield, making Shakhtar a vibrant team under Fonseca's guise.
That is a world away from the football being offered up by Allardyce, whilst PSV chief Brands has overseen the signings of players such as Kevin Strootman, Georginio Wijnaldum, Dries Mertens, Luciano Narsingh, Santiago Arias, Andres Guardado, Davy Propper, Hector Moreno, Gaston Pereiro and Hirving Lozano, helping PSV progress again.
Both Brands and Fonseca have impressive records in recent years, and would give Everton a different approach both on and off the field to Allardyce and Walsh, with Moshiri potentially on the verge of an exciting double appointment at Goodison Park this summer.