Newcastle United, Benfica and Porto have also registered interest in the 21-year-old, who forced his way into Belgium's World Cup squad and featured in their quarter-final exit to eventual champions Spain, one of four caps he has won for his country so far.
Seys was one of Club Brugge's standout performers last season, contributing five goals and eight assists from 55 appearances as the Belgian champions closed in on Champions League qualification.
Scouts from Manchester United, Arsenal and Aston Villa have reportedly attended matches to watch Seys in person, with all three clubs said to have made formal enquiries about his availability.
Club Brugge, however, are under no pressure to sell, with Seys tied to a contract that runs for another three years, and are expected to hold out for around €35m (£30m) if a deal is to be done.
That valuation is unlikely to put off United, who have identified the left-back position as an area requiring a long-term solution, though it remains unclear whether they will move for Seys this summer or prioritise other targets first.
Arsenal have carried out extensive scouting of their own, with reports handed to manager Mikel Arteta highlighting Seys' defensive solidity and his ability to add creativity down the flank at 5ft 10in.
Villa, who are on the verge of losing left-back Lucas Digne to Paris St-Germain, see Seys as a means of adding Champions League-calibre quality to the position, and are said to be particularly taken with his technical and physical attributes.
Newcastle remain interested but are understood to be behind the three Premier League rivals in the pecking order, while Benfica and Porto are both viewed as offering a strong development platform, even if they may struggle to match the financial firepower of their English competition.
Seys has made 97 appearances for Club Brugge since establishing himself in the first team, and has already started the new season with his boyhood club.