Ten Hag is battling to save his job amid mounting speculation that United's new co-owner Jim Ratcliffe plans to axe him after a turbulent season.
United finished eighth in the Premier League -- their lowest final position since 1990 -- and crashed out of the Champions League in the group stage.
The Dutch coach, who led United to their first trophy in six years when they won the League Cup last season, also clashed with Jadon Sancho and Marcus Rashford, reportedly creating a rift in the dressing room.
United have been linked with England boss Gareth Southgate, former Chelsea manager Mauricio Pochettino, departing Bayern Munich boss Thomas Tuchel and Ipswich chief Kieran McKenna.
But Ten Hag is convinced he can turn the tide by securing United's first FA Cup triumph since 2016, in the process avenging last season's loss to City at the same stage of the competition and ensuring his club qualify for Europe.
Asked on Thursday if the final could be his last match as United manager, Ten Hag laughed and told reporters: "I have nothing to say. I'm just focusing on the job I have to do.
"That is first to win the game on Saturday and then we are in the project. Keep going in the project.
"After every season you review it and see where you are in the project and what things may need to change.
"We spoke lately about it. There are players developing and values going up."
City were crowned Premier League champions for an unprecedented fourth successive season last weekend, giving them six titles in seven years.
'It's all about trophies'
Pep Guardiola's men have beaten United twice already this season and Ten Hag knows a surprise win for underdogs United would be a well-timed feather in his cap.
"It's all about trophies. We have a huge opportunity to win a trophy. In the last 10 years there has not been so many trophies at the club but we have the opportunity to win two in two years," he said.
"The FA Cup final, it's a big event. Even in a season that is not in our way, we are there. We know we have an opportunity.
"It won't be easy but we must go for it. We have to believe it. We know often against good opposition we play our best football and that must be the same on Saturday."
Ten Hag has been hampered by injuries to key players throughout the season, but his fitness issues have eased ahead of the final.
Lisandro Martinez and Raphael Varane have returned, with Victor Lindelof, Mason Mount and Anthony Martial pictured in training this week, although Harry Maguire and Luke Shaw will be sidelined.
Ten Hag insisted Maguire, who has been named in England's provisional Euro 2024 squad despite his muscle injury, had not suffered a setback.
"I don't think so, no. It's just he didn't make it, didn't heal as we expected," he said.
Marcus Rashford was left out of England's Euro squad after a poor campaign and Ten Hag challenged the United forward to prove his worth in the final.
"He looks good and that is a career, ups and downs," Ten Hag said.
"So, a down can also be fuel, that is what I see in training. He will be highly motivated. Speak with your feet, he is highly talented."
