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Van der Gaag followed ten Hag to Old Trafford last summer but turmoil back in Amsterdam could see him offered a route back.
Ajax are currently sat 16th – third from bottom – having taken just five points from their opening six games.
After ten Hag’s departure, the club appointed Alfred Schreuder as their new head coach last year but he left the role in January after a disappointing start to the season.
Former defender John Heitinga took the reins until the end of the season where Ajax failed to qualify for the Champions League for the first time since 2009.
Maurice Steijn was appointed on a three-year deal in June but his position is in doubt amid the club’s rotten start to the 2023-24 season.
United’s assistant head coach van der Gaag is in the frame to replace him, according to De Telegraaf with ten Hag understandably eager to keep him by his side in Manchester.
There has also been turmoil off the pitch at Ajax with Louis van Gaal returning to the club on an advisory basis to work alongside Michael van Praag and Leo van Wijk.
Before van Gaal’s arrival, interim director Jan van Halst was thought to be working behind the scenes to find a replacement for Steijn with van der Gaag featuring prominently on that list.
However it remains to be seen whether former United boss van Gaal would support the move.
Ten Hag meanwhile has endured a difficult start to his second season in charge with United slumped in 10th place after eight games played.
The Dutchman however is thought to have retained the full backing of the United board and the players.
United are back in action away to Sheffield United following the international break.
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