Reports in Friday's Daily Mirror have stated that under-fire chairman Ashley is to choose between Blackburn boss Ince and Tottenham number two Poyet for the job after the pair were recommended by director of football Dennis Wise.
Speculation suggests a decision could be made within the next 48 hours as Ashley seeks to quell the anger of Toon fans, many of whom are planning to protest at Newcastle's next home match against Hull City.
Ince has the more impressive CV of the two men, having done excellent jobs at Macclesfield Town and MK Dons and made a solid start with his new club Blackburn Rovers.
However, a compensation package would have to be agreed with Rovers if Ince was prised away and Poyet, a close friend of Wise's from their time together at Chelsea and Leeds, may well be the cheaper option - despite never having taken the helm at a club before.
United's caretaker boss Chris Hughton will be in charge of the team for the home tie against Hull this weekend and he has been told he may be in charge for the next three games.