According to the Daily Mail, the Hoops are now considering a move for the 44-year-old as they look for a replacement for Michael Beale, whose move to Rangers was confirmed early this week.
The Irishman is highly regarded at the Etihad after helping City’s development squad to the Premier League 2 title last season but his only experience in senior management proved far less successful.
After finishing his playing career at Rochdale, Barry-Murphy became a coach with the greater Manchester side and became caretaker manager in 2019 after the sacking of Keith Hill.
The former Sheffield Wednesday man would help the Dale stave off relegation that season and did so once again in the covid-impacted 2019/20 campaign, as Rochdale stayed up on the points per game average.
While the possession-based style of play he implemented at Spotland Stadium often earned praise from the media, particularly after some wonderful team goals in a 3-0 win over Southend in 2019, the results were far from good enough.
The 2020/21 season finally saw Rochdale succumb to relegation from League One despite scoring 61 goals, more than third-placed Blackpool who went up through the playoffs.
That campaign included a woeful record of just four home wins, as Barry-Murphy failed to find the balance between exciting attacking play and defensive stability, with the Dale recording a significant number of 0-0 draws as well as a run of three games which finished 3-3, 4-4 and 3-3.
Consistent late goals ensured that Rochdale would return to League Two and the 44-year-old was perhaps always likely to leave after that disappointment, with Manchester City poaching him for their academy set-up.
Defensive issues seem prevalent even when coaching one of the best academies in the country as the Citizens sit third in the Premier League 2 despite 18 goals against in just 11 games this season.
Hiring such an inexperienced manager, who averaged just 1.16 points per game at Rochdale in League One, would be a massive risk for QPR to take, so they should steer well clear of the Irish manager in their hunt for a Beale replacement.