Sironen hasn't played in Australia since 2021, jetting off to England to win a premiership in his maiden season at the club before securing the World Club Challenge in 13-12 win over the Penrith Panthers.
The second-rower wasn't originally supposed to start the game, however an ankle injury suffered by Joe Batchelor the week earlier promoted Sironen into a right-edge starting role where the former Sea and Tiger excelled.
Several NRL clubs reportedly made inquiries over his availability after producing a try-assist, 183 metres and 40 tackles across an 83 minute performance against the Panthers.
Fox Sports are reporting that Parramatta used their trump card in Mitchell Moses to try and lure the 29-year-old back home after the pair played three seasons together at the Wests Tigers between 2014 and 2016.
The Eels have undergone a back-row crisis, losing Shaun Lane to a broken jaw and Ryan Matterson to suspension, whilst the likes of Isaiah Papalii, Marata Niukore and Ray Stone have all departed the blue and gold army.
Sironen is off-contract at the end of 2023, however St Helens weren't eager to release the hard-running forward early, as the club aims for a fifth-consecutive premiership in the Super League.
Parramatta may still make a move to recruit Sironen for 2024, with much depending on how their new-look back-row performs this season. The club have recruited J'maine Hopgood, Jack Murchie, Matt Doorey and Jirah Momoisea for this year, and two have been thrown into the starting side already.