Coyle is considering an offer of around £500,000 for the former Hibernian forward, with the intention of partnering him alongside £3million-rated Kyle Lafferty.
Celtic, though, have kept tabs on Lafferty since having a £500,000 bid thrown out by the Turf Moor club 11 months ago.
It's understood the Parkhead outfit hope Riordan, who they rate at closer to £1m, could prove valuable in tempting Burnley to talk about a part-exchange deal for the 20-year-old when the transfer window reopens.