Over the summer, it was confirmed that the Englishman had penned a new long-term contract at Molineux, taking him through to 2028.
That development was a consequence of the Wolves board being left impressed with his first season as head coach, the team at one stage challenging for European qualification.
Although Wolves would ultimately finish in 14th position in the top flight, it was deemed to be a solid campaign having began it as relegation favourites.
However, the mood has started to change at the West Midlands outfit, initially through frustration at some of the decision-making of owners Fosun International.
There is generally an acceptance that Wolves' squad has been weakened through the departures of Max Kilman and Pedro Neto, even though replacements were found through Yerson Mosquera and Goncalo Guedes being reintegrated back into the squad.
Pressure growing on O'Neil
Nevertheless, the 3-1 defeat to Aston Villa on Saturday afternoon extended Wolves' run of just one point being recorded from their opening five games.
According to Football Insider, O'Neil is no longer viewed as irreplaceable and must find a way to turn around the club's fortunes.
That is despite the difficulty of the fixtures that have already been played, the schedule also including Arsenal, Chelsea and Newcastle United, and the matches that are to come.
Wolves next face Liverpool, Brentford and Manchester City, the onus now on O'Neil and his players to turn strong performances for parts of a match into points, and a decision could plausibly be made depending on how they fare in those games.
In their last two league fixtures, Wolves had led Newcastle and Villa, while they have scored twice against Chelsea, the Magpies and Brighton & Hove Albion (in the EFL Cup) without winning any of those games.
How far will "credit in the bank" stretch?
The report suggests that results will dictate whether the 41-year-old remains at the helm, rather than their general displays.
O'Neil allegedly still has "credit in the bank", despite losing 11 of his last 15 Premier League games dating back to March 30.
Wolves have also not kept a clean sheet in the division since February, a run spanning 17 fixtures, although they have netted in seven of their last nine games, only failing to do so at Liverpool and Arsenal.