Mary Hawgood, vice-chairwoman of The Journey trustees, said not enough people see it at its current position at Durham's Millennium Place.
She said it should be moved to near Durham Cathedral.
A spokesman for Durham County Council said the square was a key gateway for the region and many festivals and exhibitions took place there.
Mrs Hawgood added: "The Millennium Place has not developed in the way we were told it might.
"As you go down the path to the main door [of Durham Cathedral], there's a lovely big area where the Journey would look perfect and it could be the end of the journey."
"We can afford [to move] it, so it's no cost to anybody else."
Durham sculptor Fenwick Lawson's publicly funded artwork, which was installed on 22 September 2008, pays tribute to the story of St Cuthbert's coffin.
The coffin was taken from Lindisfarne, after the monks fled from a Danish invasion, and transported it to different locations, ending at Durham Cathedral at the end of the 10th Century.
A £250,000 bronze sculpture in Durham city centre is hidden from tourists, according to its trustees.