Meanwhile, Everton have continued to struggle, with Unsworth winning one of his seven games in charge and seeing them thrashed 5-1 at home by Atalanta in the Europa League before Sunday's 4-1 hiding at Southampton.
Fonseca, who has just over six months to run on his current deal, has impressed at Shakhtar since taking charge of the Ukrainian club in May 2016, boasting an impressive record of 56 wins in 73 games.
A lot of pundits are labelling Everton's start to the season as "shambolic" and "embarrassing", and having spent over £140m in the summer transfer window, it is hard to argue otherwise.
The Toffees meanwhile are now languishing in 16th position in the Premier League standings and could face the threat of relegation if things do not improve soon.
Allardyce, 63, will bring in former Leicester manager Craig Shakespeare as his chief coach as he attempts to reverse Everton's alarming slide that sees them sat 16th with just 12 points from 13 games.
Now apart of the Sky Sport's pundit team, Pardew is also believed to be a target for manager-less West Bromwich Albion, who too are looking for a spark after a poor run under former boss Tony Pulis.
The stand-in boss says Everton's players need to show more commitment to drag them away from danger.
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The Welshman is out of his third Premier League job in ten years, having been relieved of his managerial duties at West Bromwich Albion during a awful run of form, topped off by a 4-0 home defeat to Chelsea. He saved the Eagles from relegation but has since enjoyed a break from football.
Sam is very good at organising in a crisis situation and because he makes his own points loud and clear.
When confidence is low, it takes a bit of time to build it back up.
The Independent revealed on Monday that the former England manager was back in talks with the Goodison Park club after they failed to spring Marco Silva from his contract with Watford. However, despite giving no assurances about his future at Vicarage Road, Watford seem adamant that he will not be leaving.
As Everton seek to avoid the grim prospect of being relegated to the Championship, it is no surprise they have turned to Sam Allardyce to save them.
Dutchman Koeman was sacked by Everton after the club slipped to 18th in the Premier League following a 5-2 home defeat by Arsenal.