Everton had targeted Fonseca to take over, whether now or after Sam Allardyce's planned interim stint, and their owner Farhad Moshiri even met with Fonseca and agent Jorge Mendes over the weekend to discuss the move.
But Shakhtar have blocked the move for now, just as Watford stopped their Portuguese manager Marco Silva from taking over at Goodison Park.
Fonseca is in the final year of a two-year contract he signed with Shakhtar in 2016 and the Ukrainian club are still trying to convince him to sign a new one.
Fonseca is thought to be keen on a move to Everton, so much so that he turned down a possible move to Jiangsu Suning in China recently.
But so was Marco Silva, and Watford stopped him from taking over at Goodison Park even after Moshiri made clear he would pay more than £10million in compensation for the 40-year-old.
While Everton could return for Fonseca or Silva in 2018, they need a manager for the rest of this season, and they are speaking to Sam Allardyce.