CBSSports.com cited a source close to Monken that the Eagles’ fourth-year coach continued to weigh his options.
The Web site also cited a source saying as of Monday morning that interviews weren’t finished.
The Times Herald-Record, of Middletown, N.Y., reported that Monken had been offered the job but had not accepted the position.
Georgia Southern athletic director Tom Kleinlein issued a statement through the Eagles sports information department that there were no new developments between Monken and Army and that Monken was still Georgia Southern’s coach.
Phone calls to Monken and Kleinlein were not returned Monday afternoon.
Monken, 46, has accumulated a 38-16 mark in four years, including three appearances in the Football Championship Subdivision semifinals. He directed one of college football’s biggest upsets of 2013, when the Eagles knocked off Florida, 26-20, on Nov. 23.
This season, the Eagles weren’t eligible to appear in the playoffs because they were making the transition into the Football Bowl Subdivision.
Monken has experience coaching in the military setting. He was an assistant under coach Paul Johnson for six years at Navy before following Johnson to Georgia Tech.
Monken took over as coach at Georgia Southern in 2010 after Chris Hatcher was fired following the 2009 season.
He returned the triple option offense to Statesboro and turned a program that had slipped to 21-23 from 2006 to 2009 (5-6 in 2009) to 10-5 in 2010.
Monken was named the Southern Conference Coach of the Year in 2011 after the Eagles won the league’s regular season championship.
He was also an assistant under Johnson from 1997-2001, when the Eagles won FCS titles in 1999 and 2000.