Nelson Semedo is leaving Barca for Wolves and they want Dest, 19, as a replacement.
The Catalan club have made contact with Ajax sporting director Marc Overmars to discuss the conditions of a transfer.
However, Bayern Munich are also working on a deal for Dest and are currently ahead of Barca.
Barcelona are struggling financially and La Liga’s Covid-19 rules mean Spanish clubs can only buy players if they receive an equal amount of money in sales.
That is why Memphis Depay’s rumoured move to Barcelona has not yet gone ahead.
And with Semedo’s sale yet to go through, Bayern have a clear advantage in the battle for Dest.
When Dest is inevitably sold, he is expected to earn Ajax a transfer fee of €20m plus €5m in bonuses.
De Telegraaf makes it clear that Munich ‘seems to be’ Dest’s destination, but Ronald Koeman hopes he will choose Barcelona.
Dest has made 37 appearances for Ajax’s first team after coming through the club’s famous academy.
Though born in the Netherlands, Dest’s American father made him eligible to represent the USA and he has already won three caps.