Premier League interest and sign a new deal with the Eredivisie giants.
The Danish international has netted an impressive eight goals in 18 games so far this season, alerting Europe’s top clubs.
As well as the United and Chelsea, Inter Milan are also thought to be interested.
But, he is set to end speculation surrounding his future by penning a new deal at the Amsterdam ArenA.
Fischer revealed that negotiations are going well and that he expects to put pen to paper sooner rather than later:
“The negotiations are going quite smoothly and I do expect everything to be sorted out soon.” He is quoted by Sky Sports via Sported.dk.
“I don’t know when it will happen, but I’m sure it will be over very soon.”
Fischer began his career in his homeland with AGF and FC Midtjylland before moving to Ajax as a youth player in 2011.
He quickly graduated to the first-team squad, making his debut last year.
Despite his young age he has also forced his way into Denmark’s senior squad, after representing his nation at almost every youth level.