Fonseca was linked with the Toffees after Ronald Koeman was fired, but a deal could not be struck with Shakhtar for him to join.
Everton hired Sam Allardyce instead but that is looking more and more like a stop gap appointment with each passing week and a new boss is expected to arrive at Goodison Park in the summer.
If Fonseca does land the Everton job, here is a look at three players he could look to sign from current club Shakhtar Donetsk.
Shakhtar pulled off a coup when they beat Europe's elite clubs to sign Bernard in 2013.
The Brazilian international plays as a winger and at 25-years-old has his best years ahead of him.
He has scored eight times in 22 appearances this season and he is available on a free transfer this summer as he has allowed his contract to run down.
There might just be two Facundo Ferreyras.
The is one signed on loan for Newcastle three seasons ago and could not get into their first team, spending the year with the under-23s.
Remarkably it's the same player who has been scoring for fun for Shakhtar since. The Argentine has scored 20 goals in 26 games this season.
Like Bernard, his contract is also up in June and he could be worth a gamble.
Say bye bye to loanee Eliaquim Mangala, see you later to Ashley Williams and ta ra to Michael Keane.
In comes a Ukrainian bruiser to marshall Fonseca's Everton defence?
Taras Stepanenko is 28 and has made more than 200 appearances for Shakhtar, with almost 40 international caps to his name.
The centre-back could be worth a shot to freshen up a position where Everton have consistently underwhelmed this season.