Solskjaer's odds plummeted on Thursday with bookmakers across the country, coming in to around 6-4 from 25-1 following Alex McLeish's sacking.
The 39-year-old coached United's reserves for two and a half years before joining Molde, the club where he played for two years prior to moving to Old Trafford, leading them to their first Norwegian league title in 100 years last October.
He enjoyed a stunning playing career, predominantly with United where he spent 11 seasons from 1996 to 2007, scoring 126 goals in 366 appearances.
Villa owner Randy Lerner flew to the UK on Wednesday to begin the search for McLeish's successor in earnest.
Lerner said earlier in the week that under McLeish Villa lacked "compelling play and results", with his desire now to appoint a man "who sees the club's potential and embraces our collective expectations".
However, his plans are likely to have been thrown off kilter by Liverpool's sacking of Kenny Dalglish on Wednesday.
Aside from Solskjaer, other targets on Villa's radar such as Wigan's Roberto Martinez, Brendan Rodgers at Swansea and Norwich's Paul Lambert are almost certain to figure highly on Liverpool's list of prospective candidates.
Martinez spurned Villa's advances a year ago, and after his astonishing end to the season in keeping the Latics up, has been installed as one of the favourites for the vacancy at Anfield.
One man apparently not in Villa's thoughts is Mick McCarthy, dismissed by Wolves in mid-February after nearly six years in charge.