Ten Hag went into Saturday's FA Cup final against Manchester City rocked by reports that he would be dismissed regardless of the result at Wembley.
United co-owner Jim Ratcliffe and his lieutenants have reportedly sounded out several potential candidates to replace Ten Hag after the club's worst Premier League finish since 1990.
But Ten Hag gave Ratcliffe food for thought as his tactical masterclass inspired a 2-1 victory that foiled City's bid to win successive Premier League and FA Cup doubles.
United lifted the FA Cup for the first time in eight years thanks to goals from teenagers Alejandro Garnacho and Kobbie Mainoo, giving Ten Hag two trophies in his turbulent two-year reign.
Whether that will be enough to earn a stay of execution remains to be seen, with United set to conduct a review of the season before deciding Ten Hag's fate.
United's players demonstrated their support for Ten Hag with their gritty victory over City, before embracing the former Ajax boss warmly during the post-match celebrations.
And on Sunday, the 28-man first team squad published a letter -- also signed by Ten Hag -- on the club website, admitting this season has "not been good enough" as they aim to build on their unexpected Wembley triumph.
"We all know that this club is special. Yesterday's game was yet another reminder of that," the letter said.
"As we fought to win the FA Cup, the incredible atmosphere you generated inside Wembley helped push us over the line.
"Celebrating all together was beautiful. Fans, staff, players - all united as one. Those memories will live with us forever.
"It was a further reminder that with your support behind us, and the United badge on our chests, we can achieve great things."
'Excited for the future'
Ratcliffe refused to answer a question on Ten Hag's future when approached on his way out of Wembley on Saturday.
But together with directors Sir Dave Brailsford and Jean-Claude Blanc, as well as technical director Jason Wilcox, the British billionaire must give his verdict on Ten Hag soon.
The Dutch coach is believed to have jetted off on holiday on Sunday, having used his post-match press conference to warn United he will carry on winning trophies elsewhere if they sack him.
Former Chelsea boss Mauricio Pochettino, ex-Bayern Munich manager Thomas Tuchel, England coach Gareth Southgate and Ipswich chief Kieran McKenna have all been linked with the United job.
Going public with his support for Ten Hag, United centre-back Jonny Evans said: "I've only got really good things to say about him.
"Over the last month, he has shown incredible tactical flexibility. Sitting off and counter-attacking is not the style he sees himself coaching but he has recognised the right time to do it and has done it."
Regardless of who is in charge next season, United's players are determined to lift the club back to the top sooner rather than later.
"We know this season overall has not been good enough and we make no excuses. But we ended it in the best way possible, celebrating a trophy all together," they wrote.
"We want more days like yesterday. We are excited for the future here. There is so much that we have to achieve together. We will fight to bring Manchester United the success that this special club deserves."
