The Danish wide-man is currently one of Dutch football’s best young players and has been earning rave reviews for his performances for a while, despite being just 20-years-of-age.
It is understood that Spurs have been paying close attention to him in recent months, with scouts from the club having travelled to Amsterdam on multiple occasions to watch him last season.
A bid this summer is thought to be unlikely with Fischer a long-term option, but as their prospective swoop for Memphis Depay stalls efforts to land the Ajax man could intensify.
The London club have had a good relationship with the Eredivisie giants, and have used this to secure deals for Jan Vertonghen and Christian Eriksen in recent windows.
But things turned a little frosty a few months ago when the Lilywhites tracked Ajax chief Ronald de Boer to be their new manager.
Fischer is a pacey and tricky winger who had represented Denmark on six occasions.