The four concrete reliefs depict parts of a car and were installed when the building was constructed in 1969.
Mr Gosney previously said: “If the decision to demolish the car park on safety grounds is made, but at the same time if Grimsby residents feel it important for the artwork to remain as part of its community, my suggestion would then be that one of each of the four concrete panels could be preserved.”
Member of Grimsby, Cleethorpes and District Civic Society joined with Mr Gosney in calling for the artwork to be saved.
Ahead of the council giving approval for the demolition, Kerry Henderson told the BBC the artwork was “very important”.
“Art is subjective,” she said. “People have different views on it, but it is of its time and sometimes I think we look back on buildings that we have lost and think ‘oh, I wish we still had that’.”
However, Stewart Swinburn, the council’s portfolio holder for housing, infrastructure and transport, said representatives had now met with Mr Gosney to discuss “the best way forward”.
“We’ll continue to involve Mr Gosney in these discussions,” Swinburn said.
“We have agreed with Mr Gosney to see if there is a way one of each of the panels can be preserved for the future, although from the early discussions, due to the way these were integrated into the car park building, we may have to look at options other than removal of the panels.”
The authority said it was looking at possible options, including digital scanning, or taking a physical mould of the existing artwork.
