St Johnstone manager Callum Davidson has confirmed the Scottish Premiership side are interested in bringing in Dundalk defender over the winter.
The Drimnagh man, like the majority of the Lilywhites squad, is out of contract at the end of the month and is currently assessing his options.
The Lilywhites have already seen Michael Duffy, Patrick McEleney and Will Patching depart for Derry City, with more players primed for the exit door following a calamitous season in County Louth.
Defender Cleary has previously been a target for Shamrock Rovers and was offered a deal by the club after training with Stephen Bradley's side ahead of the 2018 season.
The 25-year-old has been one of the league's standout players in his four seasons at Oriel Park and his availability will have piqued the interest of Bohemians and St Patrick's Athletic.
Cleary may favour a return to Britain, however, having played youth football with Liverpool and Birmingham City before returning to Dublin four years ago.
And Davidson, a former Scotland international, confirmed he has been interested in Cleary for some time, having first made enquiries during the summer.
“Dan is someone we have been looking at,” the St Johnstone boss told Dundee's The Courier newspaper.
“I thought about him last summer but he was mid-season with Dundalk.
“We have contract offers out to a lot of players at the club so it’s a case of looking at who is staying and who is likely to be going.”
