His team in the Finnish Liiga (Finnish Elite League), Jokerit, was eliminated from the playoffs on Sunday.
Teravainen must be officially released by Jokerit in order to make the jump to the Blackhawks or their AHL affiliate in Rockford.
According to TSN Hockey Insider Bob McKenzie, Teravainen may be more likely to play for Rockford, as the Blackhaws may not have the necessary salary cap space to accommodate him on their roster.
Teravainen left an impression on the Blackhawks coaching staff prior to the start of the season and turned heads at the 2014 IIHF World Junior Championship, helping Finland capture the gold medal.
"That's something we'll talk about," Blackhawks head coach Quenneville told NHL.com of Teravainen's arrival. "We saw what he's capable of in camp, and I guess there was some real good progression to his season, as well, so you know, it could happen at some point."