The Buffalo Sabres are likely to pick the 18-year-old, who plays for Swedish league side Forlunda.
Dahlin was the youngest Olympic ice hockey player since 1984 when he took the ice for the Swedes in February at the Pyeongchang Winter Games, where Sweden finished fifth.
He also played for Sweden's runner-up squad at this year's world junior championships in January at Buffalo, dropping the final 3-1 to Canada in the Sabres' home rink. The Sabres won a league-low 25 games for an NHL-worst 62 points last season and took the top pick in the NHL Draft Lottery in April.
Rights to top unclaimed talent are distributed to clubs in the annual two-day affair, which promotes parity by allowing less successful teams first chance at promising young playmakers.
If picked, Dahlin would be just the second Swedish-born player to be taken first, after the Quebec Nordiques chose Mats Sundin with the first pick in 1989.