Demir made his first-team debut for Rapid at the end of 2019 and, despite his age, he has already become a regular in Dietmar Kuhbauer's side, making 23 appearances in all competitions this season.
The creative midfielder can also play further forward and has scored six goals in the current campaign, propelling him into the Austria under-21 set-up.
Sources told ESPN that scouts from the world's biggest teams have earmarked him as one of the brightest young players in Europe and expect a bidding war to break out at the end of the season.
Not only will Demir turn 18 in the summer, allowing him to relocate without having to depend on his parents moving with him, but he will also be moving into the final year of his deal in Austria.
Barca are well-positioned to win the race for Demir's signature, though, if they do decide to make a move for the youngster thanks to the groundwork they have laid down in recent months.
The club's scouting department has compiled an extensive report on Demir, which will be handed over to the new president, Joan Laporta, who will decide what steps to take next. The price of the deal could range from anywhere between €5 million and €15m.
As they continue to plan for the future, with a number of academy players also getting minutes under Ronald Koeman, they believe Demir would be another smart addition.
Sources at the club told ESPN there is also interest in Demir from United, City, Bayern and Dortmund but believe they have the advantage because of the player's long-standing admiration for Lionel Messi.
The left-footer has been likened to the Argentina forward and the chance to follow in his footsteps -- and possibly play alongside him if he doesn't leave when his contract expires in June -- by playing at Camp Nou is a massive draw.