Bike shelters outside the council offices will be considered subject to funding.
Cllr Noel Tuohy asked for the shelters for the large number of people visitors to the council office who have no car and for staff.
“There are so many cyclists now and people are telling me they are taking a chance leaving their bike outside County Hall.
It would be for visitors and staff. We should be encouraging people to cycle,” he said.
Cllr Willie Aird said there had been a bike shelter at County Hall, but it had been taken down because no one was using it.
“There are more people on bikes now,” Catherine Fitzgerald said.