The Goodison Park faithful are calling for the axe to fall on the Spanish boss following their 4-0 Merseyside derby drubbing against Liverpool, and a dreadful run of form which has seen them claim just two wins from their last ten league games.
Wednesday’s result at Anfield could not have come at a worse time for the underperforming Toffees, who will now prepare for a crunch FA Cup semi-final tie at home to Manchester United on Saturday.
And the fact the clash is at Goodison Park, where they have claimed just four league wins all season, is not a great omen for the Blues.
Defeat is likely to spell the end for the manager, but former Liverpool midfielder Murphy believes a cup win would make all the difference to morale and lifting the trophy at Wembley could see Martinez handed a stay of execution.
He admits, however, that supporters may not agree.
Speaking on Thursday’s Colin Murray show, Murphy said: “Roberto will be in trouble if Everton lose at the weekend, but I think the FA Cup could save him.
“I would suggest that if he wins the FA Cup, he might get the start of next season and a few months into the season to see how he does.
“I know Evertonians are at the end of their tether with the team’s performances in the last couple of months, and I have to agree last night was terrible.
“But if they win the FA Cup, something they haven’t done for a long time – well, they haven’t won any trophies for a long time – that really would change the mood somewhat.
“However, I’m saying that not being an Everton fan, of course. Would winning the FA Cup make any difference to them? Right now, after their Merseyside derby defeat, I’d say probably not.
“But, if you’re at Wembley in May and you see the trophy lifted, it might be a different feeling then.”