I just had the opportunity to meet Fabian Brunnstrom, who is at the Pepsi Center tonight to watch the Red Wings' game. Very easy person to like. He was slightly nervous, modest and tried very hard. His language skills are slightly behind those of the other Swedes on the Red Wings.
Here's the quote that stands out the most for me, Brunnstrom talking about the media build-up about his signing with an NHL team:

"This has been so big, almost like I'm the next Sidney Crosby. And I'm not the next Sidney Crosby. So I just want to sign and get it over with."

Brunnstrom said that he has no deadline as to when he will sign an NHL contract, saying that it could be tomorrow or next month. He did visit Dallas, but he won't say if he's going to visit other teams after Detroit.
He said that the thing he's looking for is an opportunity and a team that fits his style of play. He believes the Red Wings' style fits his.
Brunnstrom's hometown in Sweden is next door to the hometown of Andreas Lilja. He has spoken with the Red Wing defender a number of times before this trip.
As happened with Johan Franzen, Brunnstrom is a late-bloomer in part because of poor scouting in Sweden. Franzen, who wasn't drafted until he was 23, said that professional teams in Sweden rarely scout for talent. So it you're playing in a low division, you often don't get an opportunity to move up.
Brunnstrom said his break came when his lower-division team was playing in the same arena as Färjestads of the top division. That got him seen and into the elite league this past season.