Cerys was 11 months old when the crash happened
The parents of a man whose dangerous driving left a toddler with brain damage say they remain hopeful that her family will accept a cash "gesture".
Antonio Singh Boparan, 21, was jailed over the Sutton Coldfield crash which severely injured Cerys Edwards.
The Boparans offered £100,000 to the family, which was rejected, and £100,000 to set up a trust fund for Cerys and other children.
They added the offer was still open and hoped for further talks.
The girl's father, Gareth Edwards, from Sutton Coldfield, said he rejected the £100,000 because it was not a substantial sum in "terms of the ongoing care that Cerys needs".
The Boparan family added that it was "a private gesture" and was in no way connected to the ongoing payments from insurers.
In a statement, they said: "We met with the Edwards family several months ago to offer our assurance that we're committed to helping support Cerys long-term and have been in regular contact since.
"Our son has already expressed his deepest personal remorse at the consequences of this accident and wants to demonstrate this in a truly tangible and meaningful way.
"Therefore, he is setting up a Trust Fund for Cerys and other children who may have been injured in a similar manner and we are also depositing a lump sum into this fund."
Mr Edwards has said that he was uncomfortable about some conditions which were part of an offer, such as the jailed man being involved in fundraising.
He and his wife Tracey have received interim compensation of about £800,000 from insurers.
But the family has estimated such a figure may only last for a year and talks over further settlements were ongoing.
They are looking for a house they can specially adapt for Cerys, who needs 24-hour care, and will also need to employ a team of carers.
Cerys, who was 11 months old when the crash happened, has returned to the West Midlands after spending months at a rehabilitation unit in Surrey.
Boparan, of Little Aston, Sutton Coldfield, was jailed for 21 months in April after being convicted of dangerous driving.
He had been driving a high-powered Range Rover at 70mph in a 30mph zone in November 2006, his trial was told.
The Boparan family said some months ago Mr Edwards accepted and received an undisclosed payment from the family to enable him to take time off work to be with his family.