The 26-year-old, who has never represented the Socceroos, was a consistent performer in midfield for the Latics in 2013-14, making 50 appearances and netting five goals.
Wesolowski claimed five awards on Tuesday night including the top gong, along with the Man of the Match award and Player's Player of the Year award.
The former Australia youth international managed to remain largely injury free this season and thrived at the English League One club.
However, he faces a big decision this off-season, coming off contract and with reported interest from other clubs.
Oldham manager Lee Johnson told the Oldham Evening Chronicle he felt it was 50-50 whether Wesolowski would stay after a verbal offer.
The Latics are in the process of building a new North Stand at their home ground Boundary Park and its cost will affect the club’s ability to spend on the squad.
"I think he genuinely wants to stay," Johnson told the Oldham Evening Chronicle.
"I like Weso a lot and want to keep him. We will try to find a happy medium where everyone is content."
Wesolowski spent four years at 2013-14 Championship winners Leicester City earlier in his career but was plagued by injuries during his time at the Foxes.
The Sydney-born midfielder had loan spells at Cheltenham, Dundee United and Hamilton Academical during his time at Leicester.
Wesolowski moved to Peterborough in 2010 where he helped the club to promotion, but returned to England’s third tier with Oldham in 2011.
After initially inking a one-year deal with Oldham, Wesolowski penned a two-year extension amid interest from a number of clubs in 2012.