Louis van Gaal is known to be a fan of the midfielder and has ordered his scouting team to increase their surveillance of the 19-year-old.
Sinkgraven has been impressive form for Heerenveen this season, helping his club to sixth in the Erdivisie table.
Man United are likely to face competition if they are to sign the playmaker, with Real Madrid, Barcelona and Liverpool also interested in Sinkgraven.
However, United’s Dutch connection in van Gaal and the manager’s reputation for developing young players is believed to put the Premier League club in pole position.
Ajax also retain an interest in Sinkgraven, and the player may still prefer to move within the Eredevisie before making the leap to one of Europe’s elite clubs.
Louis van Gaal is expected to make his move for the Netherlands Under-21 International in January.