The 23-year-old has featured for Ajax in preseason but was left out of their squad for a friendly with Eintracht Frankfurt on Saturday.
Ajax coach Erik ten Hag admitted that the move was linked to developments over the player's future.
ESPN first reported United's interest in Van de Beek -- who has two years left on his Ajax contract -- in January.
The Netherlands international had been linked with a move to Barcelona in recent weeks to link up with his former national team coach Ronald Koeman.
However ESPN understands that that is not an option, with United at the front of the queue to complete a deal.
In June, Ajax director -- and former Manchester United goalkeeper -- Edwin van der Sar admitted that Van de Beek was a target for the Premier League club.
The energetic box-to-box midfielder was close to joining Real Madrid in the summer of 2019.