And talks between the two clubs have intensified in recent days with Bayern keen to sign the USA international.
There are still slight differences when it comes to a transfer fee, with Ajax requesting €30m for Dest.
Initially, Bayern only offered €10m but the two sides have come closer since then.
Dutch outlet De Telegraaf reveals that a €15m offer was turned down on Tuesday, but talks are ongoing.
Barcelona have also been linked with Dest, 19, but are not financially in a position to make a bid.
Bayern have also considered Max Aarons of Norwich for the right-back position, but have not made a concrete offer.
Should Dest arrive at the Allianz Arena, he will be the second right-back alongside Benjamin Pavard.
But the French international will now stick around after the club agreed to sell Thiago.