The chairman of the Garden Bridge Trust told Sadiq Khan in June that the charity had found an "alternative guarantor" to underwrite the maintenance costs of the bridge after the Mayor of London withdrew his support.
If the controversial pedestrian bridge between the South Bank and Temple – devised by Joanna Lumley and designed by Thomas Heatherwick – is to be built, the Garden Bridge Trust must prove to Lambeth and Westminster councils and the Port of London Authority that maintenance of the structure will be guaranteed by a third party with suitably deep pockets.
Sadiq Khan has revoked the commitment given by his predecessor Boris Johnson for the Greater London Authority to give that guarantee.
This week City Hall published a letter to Mr Khan from Lord Davies, chairman of the Garden Bridge Trust, setting out alternatives for obtaining the guarantee.
In the letter dated 19 June, Lord Davies describes how a "philanthropic foundation of appropriate standing" had declined to provide both the guarantee and extra funding for the bridge after consulting the Mayor.
He continued: "We have, however, a proposal for an alternative guarantor, which we believe will be acceptable to all parties.
"Clearly, however, the trustees cannot build such a high-profile project in the city, intended wholly for the public good, if it does not have the wholehearted support of you as our mayor."
In his response, dated 13 July, Mr Khan dodges Lord Davies's request to back an alternative guarantee scheme, reiterating instead that "the provision of guarantees for the operating and maintenance costs of the bridge would place an unacceptable financial risk on the GLA".
A Garden Bridge Trust spokeswoman told the SE1 website: "Since the Mayor decided not to continue to support the project, trustees have been looking at their all funding options carefully, and discussions have taken place with a potential benefactor and the Government. These discussions are ongoing. A decision about the future of the project will be taken soon."