Sky Germany have reported that the 19-year-old has agreed personal terms with Bayern, with only a fee between the two clubs standing in the way of a deal.
Meanwhile, new Barcelona head coach Ronald Koeman has also been credited with an interest, although the club would reportedly have to sell Nelson Semedo first to finance a deal.
Dest made a breakthrough with Ajax's senior team in 2019-20, making 20 appearances in the Eredivisie and tallying five assists.
Ten Hag said he wasn't surprised that teams have begun to circle around the US international, who came up through Ajax's famed academy.
"He is an Ajax player, he has trained and we are going to prepare for RKC," Ten Hag said at his press conference on Friday, referring to his side's Eredivisie match on Sunday. "I can't say anything about it, there is a lot of interest in all of our players. Dest has developed well so it's not surprising there is interest."
Ten Hag would go on to deny rumours that the full-back had turned down Ajax's offer of a contract extension.
"Oh, is that so?" he said when quizzed on the subject. "You make assumptions. If we have news, we will put it on our website."
Should Dest be sold, Ten Hag said that Ajax would be forced back to the transfer market for a replacement.
"If he leaves, which I prefer he doesn't, [the squad] will be thin," Ten Hag said. "Let me put it this way: I am not in favour of it but if it happens, we will look for a replacement."
Ten Hag is very familiar with Bayern Munich, having coached the club's reserve side from 2013 and 2015, and admitted that the draw of the Bundesliga champions is strong.
"Bayern Munich is a very nice club in Europe," the 50-year-old said. "I focus on Ajax and the development of Ajax. "I want [Dest] to stay. "If there is a different outcome, we'll have to change things around."