Collins' contract expired with the First Division champions and he has said he was shocked to learn that the club had called for expressions of interest in the job
The club invited expressions of interest from "suitably qualified individuals" setting a deadline of November 13 for applications.
Former Carlisle United and Bohemians manager Collins took over the reins at Lissywollen in November 2012 and guided the club to promotion by winning the Airtricity First Division title.
However, the 52-year-old's contract expired at the end of the season and he has been linked with a number of clubs, including Derry City and Sligo Rovers.
"I'm shocked to learn about the advertisement," Collins said. "I haven't been offered a job for next season, but I've been approached by other clubs and I'm entitled to speak to them because I'm out of contract.
"I've had a great time in Athlone, the players have been brilliant to me, the supporters have been brilliant to me."
Athlone Town chairman David Dully has defended the decision to advertise for the post, noting that the Dubliner's future plans remain unclear.
"We're not trying to get rid of Roddy at all," Dully told the Irish Times, "Our preference is that he stays on
"But he has been linked with other jobs and we do need to ensure that if he were to leave we wouldn't be left without a manager."