The 18-year-old was a regular fixture in the backline for his side in the League of Ireland during 2023, starting 34 matches and scoring three goals, whilst also providing one assist.
Curtis's 60th professional match for St Patrick's was the FAI Cup final against Bohemians last month, when Jon Daly's men managed to win in the showpiece event.
The right-back has been a consistent member of Ireland Under-21 squads in recent times, featuring on three occasions for his nation at youth level since his debut in August.
According to the Irish Examiner, Sheffield United have jumped to the top of the queue for the services of Curtis ahead of the January transfer window.
The report claims that the Blades are big admirers of the youngster and hope that the involvement of Keith Andrews at Bramall Lane can help convince the player to make the switch.
Chris Wilder's men are not alone in their fondness of Curtis, though, with Premier League Brighton and Liam Rosenior's Hull also in the race for the defender.
Roberto De Zerbi's Seagulls have garnered a reputation of being able to scout out the finest young talent from across the globe, and they could be looking to repeat the trick here.
Plying their trade in the Championship currently, Hull would be able to assure Curtis of more first-team involvement, however the Tigers face heavy competition for the player's signature.
It is understood that top-flight heavyweights Manchester City and Chelsea have been tracking Curtis recently, although the Blades remain in pole position for the signing.
St Patrick's supposedly want to retain the services of Curtis for one or two more years, however the Irish club realise that a move abroad is inevitable.
At just 14 years of age in 2020, the right-back made his first-team debut for Irish giants Shamrock Rovers, becoming their youngest-ever player.
Wilder's men have recent history of bringing young talent from outside of England into their youth setups, with midfielder Ryan One making the switch from Hamilton Academical in Scotland during the summer.
After coming out on the losing side of a five-goal thriller with relegation rivals Luton Town, Sheffield United face the daunting task of pitting their wits against Pep Guardiola's Man City at the Etihad on Saturday.