Ryan is set to join a Canada-based club while Quigley has had his contract cancelled by mutual agreement after a disappointing spell
Dublin native Quigley, 28, has had his contract cancelled by "mutual agreement" while Ryan, who joined the Hoops in August 2013 after a spell in Scotland with Dundee United, has made the decision to emigrate to Canada where he will continue his football career.
Quigley joined Shamrock Rovers in November 2012 on a two-year deal but, due to a series of injuries, struggled to make an impact at the club, scoring just three goals in 13 league appearances in 2013.
According to a report in the Irish Independent, Quigley is poised to re-join one of his former clubs, with the 2013 Airtricity Premier Division champions St Patrick's Athletic, Sligo Rovers and Dundalk said to be competing for his signature.
Meanwhile, Cork City have confirmed that defender Neal Horgan has committed to the club for another season.
The 34-year-old is a long-serving player at the club, first joining in 1999, and made 19 league appearances for the Leesiders in 2013.
Speaking to the club's official website, Cork City boss John Caulfield hailed Horgan as a "great servant."
"He has been a great servant to the club. He has won the league, won the cup and he is passionate about the club," said Caulfield.
"He gives us valuable experience, he can play in a number of positions, but he is also a real team player, and that is what we need at the club.