The Everton boss is under pressure from a section of the club’s support and he has a tough decision ahead of him, what with the Toffees facing Manchester United at Wembley in the FA Cup semi-final this weekend.
Does the Spaniard rest his players against Liverpool and risk a heavy beating by their on-form rivals - Or does he play his best team and risk picking up injuries for the encounter with United?
It’s a tricky situation to be in for the under-fire boss, but former Liverpool player Thompson believes both games are vitally important and thus urges Martinez to face the Reds with his best possible team.
“It's a difficult one for Everton because Martinez is under extreme pressure from the fans and there's local pride at stake,” Thompson told Sky Sports.
"He might think that the FA Cup semi-final is now the most important game but this a derby game and I know a lot of Evertonians that would say there's still a lot at stake."
"I would play the strongest team to get a result. Even a draw would be huge boost, not just for local pride but to give them confidence going into the United game.”
Everton have vastly underperformed in the Premier League this season, winning just nine of 33 matches thus far and sitting some 19 points adrift of a supposedly weak top four.
The Toffees have plenty of quality at their disposal, yet a succession of dropped points and inconsistent performances have hindered them throughout the campaign and placed pressure on Martinez.
Everton head in to the Merseyside derby without a league win in six games, scoring just four goals.