County education chiefs say they have not abandoned the idea of extending free transport to help more poorer, brighter children go to grammar school.
The plan has been under consideration as part of a package of measures aimed at improving access to grammars by less well-off families.
It has emerged a consultation on extending free transport was scrapped last year.
KCC was examining offering help to more families by raising the low income threshold to £21,000 - enabling more children to benefit from free transport.
It was also considering if it could extend its existing scheme, which subsidises travel costs for children who qualify for free school meals, to children who are eligible for pupil premium funding.
Education chiefs warned extending support could expose the authority to “significant financial risk.”
Officials say raising the income threshold would involve “challenges around how officers could reasonably and accurately means-test families to establish eligibility.”
Cllr Roger Gough (Con), cabinet member for children’s services, said the plan to extend free transport “had hit some difficulties” and there were difficulties in assessing income, partly because of the introduction of universal credit.
“It would have been difficult to assess and we may still have fallen short. We are still trying to work our way through it but at the moment, it is looking quite difficult.
"On the further option of assessment using those children who qualified for pupil premium funding, the outlook was better," said Mr Gough.
However, the council needed quite detailed information to enable it to make judgements about whether it would achieve the objective of helping less well-off families.
Cllr Gough said:“If we support children on pupil premium, would it capture those who have been classified as ‘just about managing’?
"That is people who have been on low incomes at one point but are not now or have fluctuations in their income. More work needs to be done but we are quite actively pushing that.”
A report on the progress the county council was making in improving social mobility said there was evidence grammar schools were doing more to encourage applications from poorer children.
"We are seeing grammars engaging with local primary schools and with disadvantaged children - we see this as a shared challenge...” Cllr Gough.
“We are seeing grammars engaging with local primary schools and with disadvantaged children - we see this as a shared challenge,” said Cllr Gough.
He also confirmed the council was examining if it could allow schools to do more to familiarise and prepare children to take the test.
That followed claims that independent fee-paying primary schools actively promoted their track record in getting children into selective schools through coaching.
Primary schools in the state sector are limited in what they can do to prepare children to take the test.