The 31-year-old joined the Premier League newcomers from Blackburn Rovers in the summer, featuring 118 times for the Ewood Park club over a three-year period.
Kaminski played 28 Championship matches in the 2022-23 season as Jon Dahl Tomasson's men narrowly missed out on a top-six finish, ending up in seventh behind Sunderland.
The keeper has represented his nation at youth level at the beginning of his career and has also made a number of senior squads, however he is yet to play in a match alongside the likes of Romelu Lukaku.
Speaking to Flemish outlet Het Nieuwsblad, Kaminski has revealed that a move back to Anderlecht in the Belgian Pro League could have materialised during the summer window.
"I was open to returning to Anderlecht. It is 10 minutes from my home, I have been a fan since childhood. There was brief talk about it this summer, but nothing concrete," Kaminski told the media in his homeland.
Since joining the Hatters at the beginning of the term, the veteran stopper has played in all of his side's 13 Premier League matches, however he is yet to keep a clean sheet.
Despite this, Kaminski has impressed with his performances, helping Rob Edwards's men to results against Everton, Crystal Palace, Liverpool, Nottingham Forest and Wolverhampton Wanderers.
It was common knowledge that Luton were looking to bolster their goalkeeping department ahead of their return to the top flight, with the Bedfordshire club linked with a number of targets.
West Bromwich Albion's Alex Palmer and Birmingham City's John Ruddy were among the players who were catching the eye of the top-flight newcomers, however the Hatters ultimately got their hands on Kaminski.
The Belgian featured just 21 times for Anderlecht and was sent on multiple loan spells away from Lotto Park, including to Cypriot outfit Anorthosis Famagusta and Kortrijk.
Despite failing to keep a shutout in the opening months of the Premier League season, Kaminski has only conceded 23 goals in 13 matches - the same number as allowed by eighth-placed Brighton & Hove Albion.
The Hatters recorded only their second maximum of the campaign on Saturday after a 2-1 success over Roy Hodgson's Eagles, with Teden Mengi and former Stoke City man Jacob Brown grabbing the second-half goals.
Kaminski and his Luton teammates will be aiming to earn back-to-back wins for the first time since the middle of April when they travel to Brentford in the top flight on Saturday afternoon.