The 23-year-old, who has made just 10 appearances for the Hoops this season, has been linked with a host of Championship sides but Burnley are the only club to have made a firm offer.
A £400,000 bid was rejected by Celtic but the former Hibs star would be keen on talking to the Clarets, managed by former St Johnstone boss Owen Coyle, if a fee was agreed, his agent Jim McArthur said.
McArthur claims Riordan will only make a permanent move.
McArthur told BBC Sport: "Five clubs want Derek on loan, but if he's to go it must be on a permanent basis.
"The only club to have made an official offer is Burnley for £400,000 plus add-ons.
"Derek would be very keen to speak with them if an agreement was reached."