Ajax CEO Van der Sar, talking on ESPN Netherlands' "Goedemorgen Eredivisie," spoke about the possibility of working for Manchester United in the future, their manager Erik ten Hag's new contract amid interest from Tottenham and the ill-fated Super League breakaway.
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Van der Sar confirmed he was approached by United "a couple of years ago" about a role, but with Woodward leaving in December, he has been mentioned as a possible successor.
The former goalkeeper, who won the Champions League and four Premier League titles during his six years as a player at United, was asked about these rumours and said: "It's nothing new for me, my name circulates there for a long time."
When asked if United had made contact about him potentially replacing Woodward, Van der Sar said he had not been approached.
And regarding any possible future approach, Van der Sar said he would like to finish at Ajax "in a perfect way."
He continued: "A European prize is something that triggers me."
Of his future, Van der Sar said: "[With] the work and pressure, you should have a feeling with the club. I could do the things Ronald de Boer is doing -- he works for us at Ajax and also here for you guys [ESPN]. He has more freedom than me, he has a good life.
"The pressure is different and I won't work at a club where I don't have a feeling. I could only do this for Ajax or United. I would not work for any other clubs. I am really happy with how we have [developed] Ajax in the last couple of years. We had ambitions 10 years ago to reach the top of Europe. We have reached that. We had to work really hard, we don't have a rich owner and the government didn't help us."
While he is open to working at Manchester United in the future, his immediate focus is on Ajax. This week the club announced manager Ten Hag had signed a new deal through to 2023, having been linked with the vacancy at Tottenham.
Van der Sar would not be drawn on whether Ten Hag had an exit clause in his new deal, but said "there are different options in a contract."
He said he is 100% sure Ten Hag will still be at the club next season, adding: "We wouldn't let him sign a new contract [if there was] a chance of leaving the club now."
But Van der Sar did admit Ten Hag could be swayed by a bigger club in the future.
"If he performs well, he could go to a bigger club," Van der Sar said of Ten Hag. "Everyone in the Netherlands would like to make a step to the top teams in the country. And when you are there, you want to make a step to another country. We're happy that he can work with this squad for another season."
Van der Sar also spoke to ESPN about the failed Super League breakaway. He said when the news broke on April 18, he had known nothing about it, and was "angry" with the 12 clubs. Ajax played Vitesse in the KNVB Cup final the day the news broke, and Van der Sar spoke of how instead of celebrating their 2-1 success, he was on video calls with other executives.
"I think it's strange that there weren't twenty expensive lawyers hired to look in to this," Van der Sar said. "And how it would be presented instead of something on a Sunday evening."
When Van der Sar -- who also acts as vice-chairman on the European Club Association -- was asked whether he had felt "stabbed in the back" by the breakaway clubs, he responded: "A little bit. You can also say a lot about UEFA -- UEFA is in a way a commercial company. You cannot please everybody. But their plan was good for many countries, not just a few."