The statement, issued on Kerr's Instagram account on behalf of the actor and his sister Amanda, comes more than six months after the couple were found dead.
It is unclear why it has taken so long for Mr Searle's body to be released by the French authorities or when his funeral is scheduled to take place.
Mr Kerr, who is also a country singer in the US, and his sister said that while the investigation into the deaths was ongoing they "cannot ignore the circumstances as they stand".
The statement continued: "For this reason, we must respectfully but firmly request that our mother not be included in any way in the funeral arrangements being made for Andrew."
They urged friends of their mother's not to attend the ceremony and asked people not to share photographs of Mr and Mrs Searle together.
The statement concluded: "It would be inappropriate for her memory to be associated with a service honouring the man who, based on all available evidence, may have been responsible for her death.
"We ask for understanding, privacy and respect as we continue to grieve and seek justice for our mum."
Mrs Searle's body was found in the garden of the couple's property in the hamlet of Les Pesquiès, with severe wounds to her head.
Mr Searle's body was found inside their home, about an hour north of Toulouse.
Police were alerted to the incident by a neighbour who had gone to check on them when they failed to turn up for a planned dog walk.
Post-mortem examinations confirmed Mrs Searle suffered "multiple blows to the head with a blunt and sharp-edged object" while Mr Searle died from hanging.
Mrs Searle, 56, grew up in Eyemouth in the Scottish Borders, and Mr Searle, 62, was originally from England.
They previously lived in Musselburgh, near Edinburgh, and married in France in 2023.
Prosecutors said they had lived in the Aveyron region for five years.
According to his LinkedIn page, Mr Searle previously worked in financial crime prevention at companies including Standard Life and Barclays Bank.