The 20-year old's impact helped the Swans climb into the play-offs, although they fell to a disappointing defeat to Brentford to dash their hopes of promotion.
Swansea boss Steve Cooper has openly admitted to wanting Brewster on the books for next season as they look for another promotion push in the Championship.
Speaking to Wales Online, he said: “If a loan is in Liverpool's plans for Rhian again we want to be right in there for him.
"I know he's loved already by the supporters and that's mutual. He's very well-liked around the football club. He's not just a good player – he's a really good lad."
Brewster is highly-rated among Liverpool's backroom, but another temporary move to Swansea could be likely should manager Jurgen Klopp dip into the market or feel he has sufficient options heading into the next season.
But for now, Brewster hopes he can stay with the reigning Premier League champions.
Speaking during ‘The Beautiful Game' podcast, he says he wants to stay at Anfield because "they are champions."
"Of course, I want to be at Liverpool next season, be fighting for a spot to play,” he said.
“Who is not going to want to play at the home of the champions?
"Of course, you're not really wanting to go on loan but if that's the best thing for me to do in that situation, so I'm going to get more game time then that's what I'm going to do.”
Aware of his situation within the squad, Brewster admits he is ready to accept Klopp's decision of whether he stays or goes.
He has also expressed his long-term desire of wanting to be the main striker at Anfield.
He said: “I want to play at Liverpool, I want to be 'the striker'.
"I'm just going to go to Evian and work hard and do what I can. And whatever the boss says I need to do, I'm going to accept - whether I stay, whether I go back on loan."
The Reds have been training in Austria ahead of the 2020/21 season, having cancelled their last-minute trip to Evian due to current government guidelines in France.
Here, Liverpool will set their sights on next season and play friendlies against Stuttgart and RB Salzburg. The high altitude training is designed to get the Reds back into their groove as quickly as possible.