The league has used its NFL Network to televise the games, but recently put up the 13-game series for bids and received them from NBC, Fox, CBS and ESPN. The person spoke on condition of anonymity because the bidders are not being made public.
Turner Sports has also bid, and there's a strong possibility ESPN would put the games on ABC should it be chosen by the league.
Fox has launched Fox Sports 1 and NBC has its own cable sports network, NBCSN, both of which would benefit greatly from an NFL presence.
"We'd love to have more NFL games," NBC Entertainment chairman Robert Greenblatt said at the Television Critics Association meeting in Pasadena, Calif. "Thursday night games might be really interesting to us. I just can't say. I mean, it's something we're talking about, and we have a great relationship with the NFL."
The NFL also has expressed a desire to simulcast the games on NFL Network.
NFL Network began airing an eight-game package in 2006, which increased to 13 in 2012.
Viewership for Thursday night games has been significantly lower than for other packages, but the NFL still is king of the TV ratings. Thursday night games averaged 8 million viewers on NFL Network this past season, the day's most-watched program on cable TV each week.
AP Sports Writers Rachel Cohen and Beth Harris contributed to this story.
AP NFL website: http://www.pro32.ap.org