Principal owner John W Henry and chairman Tom Werner were both in attendance for the crucial victory over Manchester City 10 days ago which strengthened the Reds' grip at the top of the Premier League.
Rivals Chelsea visit this Sunday in what could be the pivotal game in the title race but with Champions League qualification already assured FSG are set to reward Rodgers with a significant summer transfer kitty in order to strengthen his squad with the likelihood a new contract will also follow.
"I think they saw the development of the club and of the team and they were very complimentary," the Reds boss told the Liverpool Echo.
"It's important for them to see that progress across the football club.
"They are absolutely delighted with what they've seen over the past 20 months and we talked about how we can keep the club moving forward because that's vitally important.
"It's been an ongoing process since I arrived here. We don't want it to be just for this season, we want to sustain it over a longer period.
"That's something that was pretty clear for us all in the discussions we had when I came in.
"We wanted to establish something that would be in place for a long time."
Additional finances guaranteed from next season's Champions League have been bolstered by the signing of another multi-year commercial deal - this time with sandwich restaurant chain Subway - and managing director Ian Ayre is confident the club will be able to attract the best players to Anfield now they have returned to Europe's elite club competition.
"There is no question we always expected that the squad we need for next season will be very different to the squad that we have needed for this year when we were not playing in Europe," Ayre told national newspapers.
"It will cost what it costs when we decide who the manager wants to buy. That has always been on the cards. It is fairly obvious that we set out with an ambition to get into the Champions League.
"It has always been tougher in the transfer market when you are not competing at the highest level. We had the issue with Luis [Suarez] last summer because he wanted to play in the best games against the best players. That is always a factor.
"We have always been fortunate to be able to bring great players here despite that but there is no question it opens up a few doors for us and makes it a little bit easier."
A first title in 24 years is within Liverpool's grasp with three matches remaining and in that respect they have exceeded expectations this season.
"We are guaranteed Champions League football. It is an unbelievable achievement from where we were," added Ayre, referring to last year's seventh-placed finish.
"It is what we set out for but if you were taking bets at the start of the season, you'd have said fourth place would be a great achievement. Now we are guaranteed third and we are determined to push on."