The American owners have delegated responsibility to their five-man board, who will vote on Benitez's future before pre-season starts in July.
With Benitez rapidly losing support among the Kop hierarchy, his position is more vulnerable than ever.
Purslow, finance director Phil Nash and commercial director Ian Ayre can out-vote the Americans. Benitez is now fighting to keep his job in the hope his lucrative contract will shield him from the axe.
He met Purslow for clear-the-air talks earlier this week but emerged none the wiser as to whether his services will be retained.
The relationship between the pair has significantly deteriorated in recent months.
The Spanish boss has told colleagues he is yet to receive assurances significant resources will be available as the uncertainty over his role continues.
That's because it has yet to be decided if he'll be the one to splash any cash.
Liverpool are adamant there is around £15million in transfer funds for the manager.
Money raised through player sales can also be re-invested into the playing staff.
But it's inevitable recent events both on and off the pitch will heavily impact on funds.
The Merseysiders' coffers have taken a massive hit due to the failure to finish in the top four and there is no prospect of a mass influx of expensive signings.
It will only be possible to generate cash if the club's star players ask for a move, a prospect both the current manager and the board are adamant they will resist.
Benitez wants to raise funds by selling unwanted deadwood such as Albert Riera, but an exodus of more significant players can't be ruled out. Yossi Benayoun will go if Benitez stays. Javier Mascherano is the most likely superstar departure no matter who the manager.
Fernando Torres and Steven Gerrard have already confirmed they will consider their futures after the World Cup but Liverpool are confident both can be convinced to stay.
The problem for Benitez if the duo decided to force a move is that Liverpool aren't sure if the Spanish coach is the right man to re-invest the funds their sales would generate.
In fact, it's more likely their sale would assist in paying off the manager's contract.
Liverpool are undertaking a thorough review of how Benitez has used the resources at his disposal and haven't looked favourably on the last four transfer windows.
He's argued throughout that time he's been forced to work with limited funds and has missed out on targets due to the actions of his employers.
Indeed, the list of players he believes he's missed out on grows by the week. But that's prompted a perplexed reaction within, the club pointing out every significant member of the current squad except Gerrard and Jamie Carragher was bought at Benitez's insistence at a value he agreed upon.
So the game might be up for Rafa, time will tell.
