The 17-year-old is regarded as one of Sweden's brightest young talents, having made a significant impression in his fledgling career.
After making 12 appearances for Brommapojkarna, Bergvall joined fellow Swedish side Djurgardens in December last year.
During his first season with the club, the teenager went on to feature in 28 competitive matches, including 25 league appearances as he helped his side finish in fourth position.
Bergsvall scored his first senior goal in a Swedish cup game against Landskrona earlier this year, before he found the net in league matches against Halmstadts and his former club Brommapojkarna.
Having caught the eye of his club side, Bergvall made his debut for the Sweden under-21 side in October, scoring in a 4-0 win over Moldova.
While Bergvall may have made under 50 senior appearances in senior football, he is already attracting interest from the Spanish champions.
Djugardens sporting director Bo Andersson has revealed that he has held initial discussions with Barcelona about the teenage midfielder.
Speaking to Swedish outlet Fotbollskanalen, Andersson said: "Yes, I can confirm that we've been in contact and in dialogue with Barcelona.
"But it's not a negotiation yet. There was some contact with Barcelona last week but this week we haven't spoken to them."
Barcelona already have a couple of top young midfielders on their books in Spain internationals, Pedri and Gavi.
While Xavi's side keen to bring in another promisng youngster, they could face competition from clubs across Europe for Bergvall's signature.
According to Football Transfers, Manchester United, Inter Milan, Atalanta, RB Leipzig and Rennes are all believed to be showing an interest.
With Bergvall likley to be the subject of a bidding war, there is a belief that he will become Djurgardens record sale, which would require any deal to surpass the €5m (£4.3m) Dalian Professional paid to recruit Marcus Danielson in 2020.