The team was in the final stages of researching both candidates on Thursday as they were believed to be in final preparations before making an offer.
Lue, 37, has interviewed several times with the Cavs over the last month and recently met with team owner Dan Gilbert for an extended session, sources said.
Blatt, 55, had a second interview with the Cavs this week after he announced he was leaving Maccabi Tel Aviv last week. Blatt, who played collegiately at Princeton, has been one of the most successful coaches in Europe. He led Maccabi to the Euroleague title this season and coached the Russian National Team to the Bronze Medal in the 2012 Olympics.
Lue has spent the past four seasons on Doc Rivers' staff, first with the Boston Celtics and then with the Los Angeles Clippers. The Cavaliers have a plethora of young talent and the No. 1 pick in this year's draft, so they are attracted to Lue's ability to develop and relate to players, according to ESPN. He played point guard in the NBA as recently as 2009.
Cleveland is still making calls about Blatt, according to Yahoo Sports' Adrian Wojnarowski. If he doesn't wind up with the Cavs, he's expected to join Steve Kerr's staff with the Golden State Warriors.