Fulham boss Silva was forced to address speculation over his future this week following reports he could leave Craven Cottage for a move to Saudi Arabia this summer.
“Of course, there are always rumours, but what I can say to you right now is that my future is at Fulham Football Club next season,” he said.
The Portuguese knew that, realistically, his side would need to win all three of their remaining matches to claim a European spot.
But Fulham’s drop in form has come at the worst possible time.
A month ago the Cottagers were outsiders for a Champions League spot.
But four defeats in their last five matches have left Fulham’s hopes of finishing in the top half looking slim.
Silva’s side travel to high-flying Brentford next week, before finishing their campaign against Manchester City at home.
They will likely need to win both matches and hope for results to go their way elsewhere to qualify for Europe.
Should Silva keep his word and stay in west London for a fifth season, he will undoubtedly be looking to add more firepower to his squad this summer.
Jimenez scored his 13th goal in all competitions with a powerful header for the Cottagers’ opener, but Fulham lacked the clinical touch needed to score a second which would have changed the complexion of the match before Everton’s fightback.