The council wants to reallocate part of the sports lottery cash in Scotland, which it controls, to offset the high costs of keeping facilities open after hours. Spokesmen say they were given a sympathetic hearing at a meeting last week.
Estimates suggest that pound;175 million will be needed over the next five years to provide swimming pools, pitches and halls to back up sports development.
In a change of tack, the council now argues that part of the money allocated for capital projects should be channelled towards existing facilities locked up in schools.
Meanwhile, Michael O'Neill, director of education in North Lanarkshire and president of the Association of Directors of Education, told a sports council seminar at Coltness High, Wishaw, last week that ministers were misguided in backing experiments with specialist schools.
Donald Dewar, the Scottish Secretary, announced last December that pound;14 million has been set aside for pilots to develop schools of excellence for sport, the arts, science and technology.
But Mr O'Neill cautioned that setting up elite establishments would destroy comprehensive education and may not produce the expected results. "Do we want an East German system?" he asked.
North Lanarkshire's preferred model, already being developed, is to base specialist sports in particular secondaries after school. Pupils with interests and skills attend a local base for training and coaching while studying at their own school.
Mr O'Neill said: "I have grave worries about specialist schools. Does it mean that a youngster with a football ability at the age of 10 is selected after some sort of trial to go to a school and board there, away from peer group and community, and in that school to have two-thirds of their time on the normal curriculum, Standard grades and Highers, and the rest of the time being nurtured on being successful?
"What does that do for schools left behind? They will be left without the most able football players or no football team. Other youngsters who are going to be elite musicians will leave their school with no orchestra. Others in drama or dance will leave their school with no school play."
Mr O'Neill said that raising achievement for all was about self-belief, confidence, working together and role models.
Tony Gavin, head of St Margaret's Academy, Livingston, one of the country's leading Catholic headteachers, echoed the concerns. "The dangers of going down the specialist route are quite frightening if we are genuinely interested in a programme for all. It's very easy to provide a programme for some," Mr Gavin said.