The 18-year-old talent is on the books at Swedish top flight side Hammarby and scouts have flocked to watch him in action.
Swedberg, an attacker, has been scouted by both Manchester City and Manchester United, but he looks likely to be playing his football in La Liga soon.
Celta Vigo are closing in on the teenager, according to Italy-based journalist Ekrem Konur, as they shape up to win the race.
The side finished in eleventh spot in La Liga this season and if the move goes through then Swedberg will be looking to continue his development in Spain.
The attacker has made ten appearances in the ongoing Allsvenskan season for Hammarby and has chipped in with five goals.
Swedberg is able to operate through the middle or wide on the left.
He has been capped by Sweden through to Under-19 level so far and is regarded as a bright talent.
