Mr Morgan wrote to Cardiff council two weeks ago after parents from the city and the Vale of Glamorgan claimed that they were unable to access the free entitlement because of council policy, which states that if there is a maintained nursery within two miles of the family home, the child must attend that nursery.
Welsh Assembly government guidelines say the free part-time education place should be as 'accessible as possible to the child's home'.
But parents have complained that the nearest nursery is not always the most convenient - for example, if they have to take other children to schools in different areas, or if the council-run nursery does not offer full daycare and they have to leave work in the middle of the day.
Parent Jane Cross wrote to Mr Morgan, the MP for Cardiff West, after she received a letter from the council which said that as a place was now available in her nearest maintained nursery, the Michaelston ICC, she would have to enrol her three-year-old son, Ethan, there and withdraw him from a private playgroup, which he had been attending since December 2007. Otherwise, the letter said, Ethan's funding would be revoked.
Ms Cross said, 'When Ethan was one, I put his name down for both Michaelston ICC and the Cylch Meithrin Trelai playgroup. I was told there were no places available at Michaelston, so I accepted a place at Cylch Meithrin Trelai. It took a long time to get him settled and I am not prepared to uproot him.'
Mr Morgan's letter to Cardiff council queried its policy and said, 'It seems a bit harsh, if a child is well settled after ten months at one nursery, to be told that they have got to switch to another nursery or be reclassified as a private pupil.'
He added that the policy seemed 'contrary to good educational nursery-age practice to move a child simply when places become available'.
A Cardiff council spokesperson said, 'Parents are free to choose a nursery from a range of providers and at a range of locations. The council will not fund places with private providers when it can offer excellent local facilities to all local families. However, consideration will be given to extenuating social circumstances which compromise a parent's ability to take up a nursery provision offered.'
Sandra Welsby, national development manager of NDNA Cymru, said she was not aware of any other councils in Wales that had the same policy.