Speaking to Sky News on Monday, Ashley said it was "possible" a sale could be completed "before the January transfer window", although he wasn't in exclusive negotiations with an interested party.
Walsall-born Sports Direct owner Ashley, 54, put Newcastle up for sale in October 2017.
Asked about the likelihood of the month-long timeframe being met, he described it as "possible", stopping short of calling it realistic - saying it was "too strong a word".
The Newcastle boss said he is "hopeful" of stepping aside to find an owner "that will please everybody".
Ashley pulled out of talks with Amanda Staveley's PCP Capital Partners in January after failing to strike a deal, while former Manchester United and Chelsea chief executive Peter Kenyon is also understood to have expressed an interest in putting together a consortium to buy out Ashley.
Benitez's side lost 3-0 at home to West Ham on Saturday, a result which ended a run of three successive victories, their first of the season after a hard start. "Hopefully we can carry on our recent good form and get the deal done".
However, a report from Luke Edwards at the Telegraph might offer Newcastle fans more concrete hope than ever.
After taking just three points from their opening ten games, Benitez's side have improved recently, winning three successive games before West Ham eased past them at St James' Park.
There are rumours circulating that Ashely, via his lawyers, has spoken with buyers but is yet to see evidence of proof of funds, whilst some senior Newcastle staff members are believed to be "skeptical" about how honest Ashley was during his Sky interview.