Louis van Gaal refused to discuss his future at Manchester United as speculation linking Jose Mourinho with the Old Trafford post intensified on Saturday.
The build-up to the FA Cup final was overshadowed by a report in Spanish newspaper AS that Van Gaal would be dismissed and replaced by the Portuguese in the immediate aftermath of the game at Wembley.
While that scenario did not materialise, talk of Van Gaal's impending departure increased despite United securing a 2-1 extra-time victory over Crystal Palace to give the Dutchman the first major trophy of his two-year spell in charge.
Asked if he feared he was about to lose his job, Van Gaal told a news conference: "I show you the cup, and don't discuss it with my friends in the media, who [have] sacked me for six months.
"I don't want to talk about leaving the club."
Earlier, speaking to BT Sport, Van Gaal hinted at his desire to stay on.
Asked if he would be back next season, he said: "I hope to see you."
The 64-year-old added: "I want to win things, titles. I have won everywhere I have worked so I don't have to prove myself. When they want to use my knowledge and my management, then I shall continue because we have proved again that we have a title.
"Even in the time of Alex Ferguson, he did not win every title."
Questioned if he feared glory was slipping from his grasp when Chris Smalling picked up a second yellow just before the end of the first half of extra time, Van Gaal said: "Of course, because with 10 players and we have played Tuesday evening [against AFC Bournemouth] also, but we have deserved it I think."
Jesse Lingard went on to grab the winner for United, for whom Juan Mata cancelled out Jason Puncheon's opener.