Aldershot are currently flying high in League Two, sitting inside the play-off positions in 7th place, and are keen to bolster their ranks in the January transfer window.
O’Leary is out of contract at the end of the season, and, according to the GetHampshire newspaper, has been told he can leave Swansea in a bid to find a new club.
The Welshman has made just 1 appearance – in the FA Cup vs Horsham – since the Swans have returned to the Championship club and was on loan at Leyton Orient earlier this season.
32 year old O’Leary has made over 300 appearances for the Swans since making his debut in 1996.