The 25-year-old Serbia international has become the Giallorossi's undisputed number one for the 2024-25 campaign after a couple of seasons on the periphery of the team, taking over from Rui Patricio.
Svilar has kept three clean sheets in his first seven Serie A appearances of the new campaign, and he was also Roma's first choice in between the sticks during their deep Europa League run last season.
In total, the Belgian-born youngster - who came through the Anderlecht youth setup - boasts 14 clean sheets in 43 matches for the Italian giants, who signed him on a free transfer in 2022 after his exit from Benfica.
Roma still have Svilar under contract for another three years, but according to AS Roma Live, all of Manchester City, Liverpool and Newcastle United are now keeping tabs on his situation.
Liverpool 'quoted £33.5m' for Svilar
Man City were close to losing Ederson to Saudi Arabia in the summer before the Brazilian elected to stay on, although his long-term future remains the subject of much uncertainty.
Meanwhile, Liverpool number one Alisson Becker and Newcastle's first-choice Nick Pope are both in their 30s, and Svilar would represent a far younger alternative to the experienced pair.
However, as Roma are under little pressure to let the Serbian depart, they have reportedly slapped a price tag of between €35m (£29.3m) and €40m (£33.5m) on the head of their top goalkeeper.
Roma would also be well-placed to demand more if he continues to improve, but both Liverpool and Newcastle are said to have asked for 'preliminary information' through intermediaries to gauge Svilar's interest in a summer move.
The ex-Benfica man is said to be "very happy" in Serie A, though, and he would only consider moving on if the offer was too good to refuse on both his and the club's side.
Why Svilar could ultimately opt against Liverpool move
Goalkeepers moving from Roma to Liverpool and becoming a huge success on Merseyside is not a novelty - after all, Alisson followed that exact path to greatness six years ago.
The Brazilian is now being bedevilled by increasingly frequent injury problems, though, and his latest hamstring issue is expected to rule him out for around six weeks.
A departure in 2025 is therefore not totally beyond the realm of possibility amid links with Saudi Arabia, but Liverpool have already planned for his exit with the capture of Giorgi Mamardashvili.
There is a consensus that the Georgia international will eventually become number one at Anfield, so Svilar may have to be content with a second-string role, especially if both Alisson and Caoimhin Kelleher leave next summer.
As a result, the Roma man may wish to make a move to a Premier League club that can offer him assurances over game time, or stay at Stadio Olimpico and continue to develop in Italy for another year or two.