Burnley manager Sean Dyche says striker Danny Ings will not be fazed about facing Liverpool on Wednesday night
The former Chelsea boss, currently at Real Madrid, was cut to 4/1 from 33/1 by Sky Bet as a result of the support. He later drifted back out to 5/1.
Several national newspapers had linked the Italian with the post, vacated on Tuesday by David Moyes.
Sky Bet's Marcus Berry said: "We started to see money on Ancelotti from around 11pm last night at 16/1 and we have seen a steady stream which has carried on this morning and meant his price has shortened.
"I can see this market having many twists and turns before someone is appointed though."
Real are currently third in the Spanish league and face Bayern Munich in the Champions League semi-finals over the next week.
Louis van Gaal remained odds-on and was being offered at 4/5 on Wednesday evening having been backed in following Moyes' sacking on Tuesday.
The Netherlands coach is due to lead the Dutch at the World Cup this summer. That could make an appointment by United tricky as he could potentially be in Brazil until mid-July.
Unlike Moyes, both Ancelotti and Van Gaal have a proven track record of success at the highest level.
Ancelotti is a two-time Champions League winner with Juventus and won the Premier League during his time in charge of Chelsea.
Van Gaal won the Champions League with Ajax and has also won the Spanish and German league titles with Barcelona and Bayern Munich respectively.
The market suggests the race is a two-horse one with Sky Bet offering at least 14/1 about any of the other candidates.
- Posted at 1000 BST; updated at 1920 BST on 23/04/2014.