The 29-year-old arrived at Carrington on Friday morning, having already undergone an assessment of his troublesome knee on Thursday.
Owen is expected to have further tests at a Manchester hospital later and if United's medical staff give him the all-clear, he could join former club Liverpool's arch-rivals as soon as next week.
Owen's Newcastle contract lapsed on July 1 but although the former Liverpool and Real Madrid striker apparently remained eager to stay in the Premier League, it appeared only the likes of Stoke and Hull were ready to make a concrete offer.