Vic Haines, 64, has listed the bike, valued at £10,000, on the online auction site.
The model is almost identical to Mr Obree’s self-built “Old Faithful”, on which he twice broke the record for the greatest distance cycled in one hour.
Mr Haines said: “This bike is the Rolls Royce, the best you can get. I kept it and put it on the wall, I removed the chain and the wheels and it became a piece of objective art.”
Links to the eBay auction were retweeted from Graeme Obree’s Twitter page.
His spokesman added: “It’s Vic’s bike to sell. It’s a cool looking bike, Vic’s kept it in pretty good condition. I hope it goes for plenty.”