Councillor Johnston has sent a letter with 16 questions to council leader Jim Logue and chief executive Des Murray, and Campsies Centre chairman Alan Graham.
He said: “The council lawyer’s position is that the clock does not belong to the people of Cumbernauld, but is owned by Bridges Antonine, owners of the Antonine Centre.
“I find this view totally unacceptable, the clock was a clear gift to the people of Cumbernauld by the Raymond Giilies Foundation in 1977.
“If Network Rail contact Bridges Antonine to try to take the clock away, does the council simply regard this as a private business matter, or do they intervene to halt such a move?
“We need clarity on whether the council will ensure the St Enoch Clock belongs to the people of Cumbernauld.”
A council spokesperson responded: “We have advised Councillor Johnston that, following investigation of the ownership of the St Enoch clock, we believe it has come to form part of the building in which it is located and therefore is owned by Bridges Antonine.
“However, Campsies Centre has historically maintained the clock and is actively working with the council and the Antonine Centre to find a suitable permanent home for the clock.”
Councillor Johnston is also writing to Network Rail and Bridges Antonine regarding the matter.