Parise, 27, said later Monday that he has not made up his mind, and his agent said he narrowed his choices to a select few teams.
Goaltender Martin Brodeur also received interest from the Hawks before re-signing with the Devils on Monday.
Parise had 31 goals and 38 assists last season while leading the Devils to the Stanley Cup finals. He's a former 45-goal scorer who would instantly make the Hawks the most dangerous offensive team in the Western Conference. His leadership skills are also highly touted as the captain of the Devils in 2011-2012.