United are understood to be keen to bring Ashworth to Old Trafford as part of an overhaul of the club's structure following Jim Ratcliffe's deal to acquire a 25 percent stake and take control of football operations.
The chairman of chemicals giant INEOS has moved quickly to strengthen United's football leadership group, with recruitment a particular area of focus.
Britain's Press Association news agency said Ashworth, who was previously Football Association technical director before taking up a similar position at Brighton, had stepped away from his duties at St James' Park.
Ashworth, who has been in post at St James' Park for 20 months, was a key appointment by the Magpies' new Saudi-backed owners after they completed their takeover of the club in October 2021.
Some of Ashworth's signings during his time at St James' Park include Swedish forward Alexander Isak, Italian midfielder Sandro Tonali and wingers Anthony Gordon and Harvey Barnes.
It is understood there has not yet been formal contact between the Premier League clubs, and Ashworth was in the stands at St James' Park on Saturday as Eddie Howe's men played out a 2-2 draw with Bournemouth.
Howe admitted Friday that he had "concerns" over Ashworth's knowledge of the club's inner workings as speculation mounted over his interest in the Old Trafford job.
"We are naturally disappointed that Dan has chosen to leave, however our exciting journey doesn't stop and the process to recruit a new sporting director will begin immediately," Newcastle CEO Darren Eales said in a statement.
"We thank Dan for his efforts at Newcastle United and we wish him and his family well for the future."
Reports said Newcastle want £20 million ($25 million) in compensation and that in the absence of a deal Ashworth may not be able to start a new job until early 2026.
