The Eels are on the hunt for a new coach after sacking longstanding mentor Brad Arthur after his side slumped to a 3-7 record; the latest heavy loss coming at the hands of Bellamy's men during Magic Round.
Parramatta went after Dolphins coach Wayne Bennett to replace Arthur but the veteran super-coach was committed to rejoining South Sydney for the 2025 season.
After missing out on their first choice, the former powerhouse club insisted they were in no rush to name a new coach, with Trent Barrett taking over this season in an interim role.
But chief executive Jim Sarantinos admitted they had started compiling a list of prospective candidates, with the highly-credentialed Ryles a certainty to be among them.
Ryles was part of Melbourne's premiership success in 2017 as well as helping the Storm reach two other grand finals.
He left to join the England rugby team's coaching staff under Eddie Jones but that was curtailed by COVID-19 and then he signed on as an assistant with the Sydney Roosters.
Ryles was cut from that job in mid-2023 after he was linked with a return to Melbourne, and again spent time working with Jones, who took the Wallabies to the Rugby World Cup.
Bellamy said Ryles was a valuable member of the Storm staff.
"He's doing a really good job for us," Bellamy told AAP on Wednesday.
"He's doing some defence with our ruck but he's also taken on the role as leadership coach and a bit in recruitment.
"We're mixing things up for him."
Craig Bellamy knows better than anyone that NRL head coaching vacancies are rare. (Joel Carrett/AAP PHOTOS)
Bellamy, who recently announced he would remain at the Storm helm for 2025, said he didn't want to lose Ryles to the Eels but accepted that NRL head coaching vacancies were rare.
Arthur was also an assistant to Bellamy at Melbourne before joining Parramatta in 2011.
"It's not in my control ... we're not going to concern ourselves with things that we don't know are going to happen," Bellamy said of the possibility of losing Ryles.
"We don't want him to go but it's not very often that you get those sort of opportunities so if he wanted to go I wouldn't imagine we would stand in his way."
Arthur spoke after his brutal axing, saying he had no bitterness towards the Eels.
I've really enjoyed my time and I'm really grateful for my time, I don't hold any resentment, I'm not bitter about what's happened," he told FoxSports' NRL360.
"Parramatta's a massive club so I've gotten used to it (the pressure), so I know whatever's next for me I'm going to be better again.
"I'm proud of where I started to where I am now. In 11 years, we've played in finals, hopefully I've contributed to changing people's lives."
Bellamy said he expected Arthur to land another role when he was ready.
"I'm sure he will find another club - he's a good coach and really good person so he will find another job," Bellamy said.
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