The man was found around 7.20am off Craw Road near the hospital.
The death is currently being treated as unexplained and enquiries are ongoing to establish the full circumstances.
The man is described as being white, between 20 to 30-years-old and of thin build.
He has the word 'Stephen' tattooed on his inner right forearm and a design including the word 'Mum' and a green rose on the outer left forearm.
He was wearing a blue hooded top with a zip, black tracksuit bottoms and black Nike trainers. He was also wearing a crucifix around his neck.
Police Scotland say they have been working to identify the man but have so far been unable to successfully do so.
But it is hoped that a member of the public may come forward who can help.
Detective Inspector Ian Ross of Paisley Police Station said: "Sadly, despite our enquiries so far, we have been unable to identify this man.
"We want to establish his identity in order to update his next of kin.
"We are liaising with NHS Greater Glasgow and Clyde as part of these enquiries and the man is not believed to have been a patient at the Royal Alexandra Hospital on Wednesday.
"I would urge anyone who believes they may be able to assist to contact 101 as soon as possible, quoting incident 0409 of 24 March."