Speaking in Scotland, Reeves said protection for women-only spaces would "absolutely stay", adding: "We're not going to be changing anything around biological sex ... we're really happy to talk to JK Rowling to give her assurances about that."
But Rowling said the meeting was conditional on Labour first meeting a series of groups from across the UK that she supported.
The shadow chancellor made the offer to meet the author and former Labour donor yesterday, after Rowling said she would "struggle to support" the party in next week's general election.
Labour has reiterated its pledge to "modernise" the process under which people can change gender, removing what it termed outdated elements of the process, such as requiring consent from a spouse. The requirement to present evidence showing a person has lived as their new gender for two years would be replaced with a so-called reflection period lasting the same amount of time.
The plan is largely the same as that outlined last year by Labour's national policy forum, but was reported by the Times after an article for the paper on Saturday by Rowling expressed her unease with the party's position.
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