Armstrong did not start for Celtic against Partick Thistle away from home at the Firhill Stadium in the Scottish Premiership on Friday evening.
The 25-year-old midfielder came on as a substitute in the 78th minute, as the Glasgow giants won 1-0 to maintain their strong start to the season.
The Scotland international played brilliantly last season, but the midfielder has struggled to recapture that form so far this campaign.
Armstrong has been linked with moves away from Celtic Park in the summer transfer window, with Premier League clubs Southampton, West Bromwich Albion and Everton interested in him, according to The Express.
“Stuart’s position will be sorted one way or another,” Rodgers told The Daily Record. “He was terrific last season and unfortunately, this is effecting his game. It needs to be resolved one way or another."