The 18-year-old has been attracting interest from across Europe and is expected to leave the Swedish club when the January transfer window opens.
Dahlberg is understood to have met with representatives from Watford at their London Colney complex on Tuesday as the Premier League club attempt to seal a £3million deal.
However, reports claim that he is also set to meet with officials from Arsenal and Napoli in the coming days before making a final decision on his future.
The Swedish under-21 international is regarded as the brightest goalkeeping talent to emerge from the northern European nation for many years, and he has been tipped to force his way into the senior squad for the 2018 World Cup.
Watford currently have Heurelho Gomes and Daniel Bachmann in their squad, while Greek international Orestis Karnezis is also on loan from Udinese.