Ashworth is being targeted by Manchester United as part of Sir Jim Ratcliffe's Old Trafford shake-up after purchasing a 25 percent stake in the club.
The former Brighton technical director who is credited with the transfers of Magpies stars Sandro Tonali, Sven Botman, Anthony Gordon and Alexander Isak, is believed to be keen on joining Man United's newly-formed hierarchy.
As yet, nothing has been agreed between Ashworth and the Red Devils but, with Newcastle already planning future moves in the transfer market and Ashworth privy to the club's financial situation, Howe wants clarity as soon as possible.
"Yeah, it's quite an unusual situation," Howe told his pre-match press conference on Friday ahead of Newcastle's clash with Bournemouth.
"Usually there's transfer speculation on players, this is very different. Whatever happens, we want a quick resolution."
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The Magpies boss stopped short of directing any level of praise at Ashworth when asked whether his potential exit would be a blow to the club.
Instead, Howe told reporters that continuity is key to success for sporting directors - in what could be perceived as a bit of a dig at Ashworth, who joined the club in February 2022.
"It's a difficult one because when you're in that role you need longevity to actually see the fruits of your labour, it's sort of a long-term position," the manager added.
"I think the people that have done it best in the Premier League throughout time have always had a period of stability.
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"Change takes a long time in any football club to get those processes exactly how you want them to be.
"Dan's had a relatively short time here but let's see what happens. As I sit here nothing's happened."
Howe was quick to reassure Newcastle fans that the club will continue to run efficiently in the event of Ashworth's exit.
"Football always moves on very quickly and I'd say that regarding the manager's position," he said. "Newcastle is a huge football club who will continue to works in a very efficient way regardless of who's here.
"We've got some very, very capable people here in all departments so we would carry on very smoothly.
"I think there has to be a succession plan for everybody. "