Just how much time, is a matter for conjecture, but it seems as though the club's owners have become seriously disenchanted with changing horses in mid-stream, and will either give the Northern Irishman sufficient time and space, or enough rope - depending on how positive one feels about the future.
Rodgers has already rung the changes - doing his best to quietly dismantle the squad put together (at some expense) by Kenny Dalglish. Jordan Henderson and Stewart Downing appear to have become peripheral, while Charlie Adam and Andy Carroll have been shipped out (the latter perhaps temporarily) while Joe Allen has been brought in - an emblem of the style of football Rodgers believes in and wants his sides to replicate.
It's too early in the season to talk about whether it's working or not, but there's no escaping the fact that Liverpool have yet to win a league game, and have already been beaten twice. It is the worst start to a league season since 1911, and while statistics and historical notes are there to be ignored, the facts and the figures at the commencement of the new era at Liverpool will not sit well on Rodgers' current CV.
Redemption and a massive boost for the club could be on hand though this weekend, when they entertain Manchester United at Anfield.
Clashes between the two clubs are massive events in the football calendar, irrespective of the fact that Liverpool haven't won a league title since 1990, while Manchester United, between then and now, have picked up no less than....12.
Over the years it has become one of the greatest rivalries in world football, the antecedents of which date back to a city rivalry cemented and exacerbated by the building of the Manchester Ship Canal (completed in 1894).
I'll spare us all the history lesson, but the construction of the canal was excellent financial news for Manchester, and brutally disappointing for the people of Liverpool. It's fair to say that antipathy between the two cities has existed ever since, and the football clubs seem to have had no alternative other than to take up the gauntlet.
Sir Alex Ferguson continues to refer to these encounters as his favourite games in football, although there can be little doubt that his team's ascendancy in the last two decades, combined with Liverpool's lack of success, has contributed hugely to his overall sense of satisfaction.
In the wake of recent published findings relating to culpability for the 1989 Hillsborough disaster, exonerating Liverpool fans - despite what the authorities contrived to say at the time - Anfield will be brimming with emotional fervour on Sunday as the two teams meet.
There's every chance that, in the circumstances, football will take a back seat, as people in the city come to terms with the fact that what they already knew has finally been accepted as the truth - after 23 years of asking.
Passion and intensity will be in no short supply, and if Brendan Rodgers can find a way of harnessing it for the benefit of his players, we could be about to witness something special.
Once again, depending on which way you look at it, this latest edition of the Liverpool versus Manchester United rivalry couldn't have come at a better, or worse time.
Rodgers has been keen to point out that his project is a work in progress, and he'll be relieved to know that the Anfield faithful are 1) faithful, and 2) patient...as long as they're starting to like what they see, and believe that the direction the club is going in is the right one.
Roy Hodgson, for all his qualities, didn't even try to treat fans to the style to which they have become accustomed, while a chorus of disapprovers denigrated Kenny Dalglish for his tactical naivety and out-of-touch philosophy (I know...it's almost blasphemous, right?)
Rodgers will be given time, not only by the fans, but also by the owners, and there can be little doubt that a win against their arch rivals on Sunday will go a huge way to endearing the new manager to a bunch of supporters who are among the most loyal and passionate in the world.
Despite Sir Alex Ferguson's assurances that Manchester United as a club will support Liverpool "in every way we can", on Sunday, don't except that sentiment to extend to giving their opponents any quarter on the pitch. United, as always, will go all out for the win, and there's nothing Ferguson enjoys more than a win over Liverpool - whatever the circumstances.
For Liverpool however, a win on Sunday, with the backdrop and context taken into consideration, would create the kind of feel good factor that's been missing on the red part of Merseyside for far too long.