After playing exhibition matches in North America in 1957, Alexandrov was put on the negotiation list of the Chicago Black Hawks, a team in the National Hockey League. While Soviet players were not expected to be able to move to North America, Chicago still felt highly enough of him to do so in the event that changed. He was inducted into the IIHF Hall of Fame in 2007.
Following his participation in exhibition matches across North America in 1957, Alexandrov was considered for a potential transfer to the Chicago Black Hawks of the National Hockey League. Although it was thought unlikely that Soviet players would be allowed to relocate to North America, Chicago's interest in him remained strong enough to warrant consideration.