The Premier League's bottom club have yet to confirm who will take over from Mike Phelan, who was sacked on Tuesday.
Reports suggest former Olympiakos boss Marco Silva has been lined up, while former Birmingham City manager Gary Rowett was an early favourite.
Ashbee, who played for the Tigers between 2002 and 2011, told the Press Association: "It's a poisoned chalice."
He continued: "I don't think Gary Rowett is going to take it.
"I think someone from overseas will be appointed. Someone who isn't aware of what's been going on."
Portuguese Silva quit Olympiakos for personal reasons in the summer after guiding them to the Greek title, and also won promotion to the Portuguese top flight with Estoril before a brief spell at Sporting Lisbon.
Vice-chairman Ehab Allam said on Hull's website the club hope to name their new manager before the weekend. Hull host Swansea in the FA Cup third round on Saturday.
"They need to get the new guy in sooner rather than later," said Ashbee
"He's got good stock from overseas, but has no experience of the Premier League.
"It's a difficult task even if he had the whole of pre-season to put his plans in place, but it would appear to be impossible now."
It has been a tumultuous season for Hull, who are up for sale. In July, Steve Bruce left as manager after his relationship with Allam broke down.
Phelan was placed in temporary charge and, even though he had only 13 fit senior players at his disposal, his side marked their Premier League return with successive wins and he was named manager of the month for August.
However, the Tigers are now three points from safety and without a league win since 6 November.
Commenting on the situation, former Hull manager Phil Brown told BBC Radio 5 live: "It's not just about relegation as far as Hull are concerned. The fans are worried about their club.
"The stadium was a fortress when I was there and the fans kept us in the league. Now it's known as the library. It's scandalous what's happened to the club.
"There has to be joined-up thinking in wanting to take the club forward."
The new Hull City manager is facing an "impossible task", according to former captain Ian Ashbee.