Fabrizio Romano reported the approach, noting Liverpool are weighing up two options: signing the 18-year-old immediately, or structuring a deal that would see him arrive at Anfield in 2027.
The timing is closely tied to Giorgi Mamardashvili's own situation, with Nottingham Forest having emerged as serious suitors for the Georgian, who has established himself as Liverpool's clear number two behind Alisson since his move from Valencia.
Brughmans, at 6ft 7in, has already broken into Genk's first team this season and is regarded as one of the most promising young goalkeepers to come through Belgian football in recent years, having progressed through every age group from the Under-15s up before earning the Under-19 captaincy.
He has made 15 senior appearances for Genk, though results in the current campaign have been mixed, with Brughmans conceding eight goals in four league matches as Genk sit seventh in the Belgian top flight. Liverpool are not alone in their interest - Bayern Munich, managed by Brughmans' fellow countryman Vincent Kompany, have also been credited with monitoring the goalkeeper.
Should Liverpool proceed with an immediate deal, it would represent a significant show of faith in an 18-year-old with limited senior experience, particularly given Alisson's injury record in recent seasons has meant his understudy has regularly been required to step in at short notice.
The alternative - agreeing terms now but delaying his arrival until 2027 - would allow Brughmans to continue developing at Genk while giving Liverpool first refusal on one of European football's most closely watched young goalkeeping prospects.
Brughmans joined Genk's academy from PSV in 2022 having also spent time with Royal Antwerp as a youngster, and signed a contract extension only weeks ago that ties him to the Belgian club until 2030 - a deal that would need to be renegotiated as part of any Liverpool move.
His combination of physical stature and technical development from an academy that has also produced Thibaut Courtois and Mike Penders has made him a closely tracked figure in Belgian football circles, even before his senior breakthrough this season.