As reported in last week's Visitor, property developer Chris Tudor Whelan has been finding out how much the stone is worth, saying he wants to cover the cost to him of its excavation.
He has said he'd like it to stay in the city but couldn't give any guarantee. He has consulted Sotheby's whose New York office, which deals with many such sales, says it could fetch up to $100,000.
Now the leader of the city council has stepped into the controversy.
Coun Ian Barker has written to the Secretary of State for Culture Media and Sport, Tessa Jowell, asking her to refuse an export licence if there's any suggestion it's sold abroad.
Coun Barker said that, as far as the city council was concerned, planning permission was granted with archaeological conditions attached. There was an obligation in the development agreement not to dispose of any important archaeological finds.
Coun Barker said: "No one could have anticipated finding a stone of such significance, but it was known that this could be an important archaeological site.
"Planning permission was only granted on condition that a proper archaeological investigation was carried out. The costs of this should have been built into the development, so it's more than a little opportunistic to seek to recover them just because something really important has been found.
"This stone is an important relic of Lancaster's Roman past. In my view it should stay in Lancaster and the public should be able to see it. It shouldn't be sold into a private collection or sent abroad.
"I will certainly be asking officers of the city and the county councils to do all they can to enforce the obligations attached to the planning consent.
"I've asked Tessa Jowell to refuse an export licence if this is sold abroad, so that we have a chance to keep the gravestone in Lancaster."
The stone is about 2,000 years old and depicts a Roman horseman holding the head of a slain victim.