Earlier in the debate, she had said "we recognise that the leaver destinations for looked-after young people and careleavers are significantly poorer than their peers".
"It seems to me it is going to be inevitable that there should be a fit and proper qualification for anyone who is going to be involved in football administration, " said Leaver.
For example, the prime minister suggested it was unfair that an unemployed school leaver can claim housing benefit whereas one who finds work or who goes on to university is unable to claim housing benefit.
On education, he said he wanted the system to be "like the pushiest, most sharp-elbowed, ambitious parent there is" and he wanted it to "be the norm" for every school leaver to start an apprenticeship or go to university.
"In recognition of the increased resources needed to support teaching in some schools, over the past two school years, 14 schools in areas of greatest deprivation have each had their staffing formula increased by one teacher, " said Mr Leaver.