Staff and buildings at Carsemeadow nursery near Quarriers village were transferred by Strathclyde Region to Inverclyde, one of Strathclyde's 12 successor councils. But the budget remains under the control of Renfrewshire as the majority user, with 80 per cent of the pupils at the school.
Renfrewshire's first education committee meeting was told this week that the councils had reached deadlock. An interim arrangement will allow the nursery to function until July next year.
An independent admissions panel will have representatives from both councils.
Brian Oldrey, education convener on the Labour-run council, said: "We are still arguing about who this property belongs to. My ideal would be for it to revert to Renfrewshire."
Mr Oldrey warned: "If the decision comes back from the Property Commission that we do not gain control, then we will put forward plans to spend that money within our own boundaries."
Renfrewshire has pledged to provide a pre-school place for every four-year-old, and eventually for every three-year-old, through partnerships with the private and voluntary sectors. Despite a 10 per cent cut in grants to the voluntary sector, the council decided this week to give more than Pounds 44,000 to pre-five voluntary providers.
Carsemeadow nursery has the space to double in size, but a move by Scottish National Party councillors to expand it by half, creating 60 part-time places, was defeated by 15 votes to six.
Mr Oldrey said that the area served by Carsemeadow was not a priority.
* South Ayrshire, which is not taking part in the Government's nursery vouchers pilot, will expand provision in August by 266 part-time places to a total of 1,015.