Vance arrived in the UK last week and met David Lammy for talks about Gaza and other international affairs at the foreign secretary's official residence, Chevening House, in Kent on Friday.
The vice-president is not due to meet Conservative leader Kemi Badenoch, who was speaking to business owners in the Isle of Wight on Tuesday.
A Conservative spokesman said aides for Badenoch and Vance had been discussing a meeting but "just couldn't make it work with schedules".
Badenoch met Vance last year when she was in Washington DC and had dinner with the vice-president.
Jenrick, who was defeated by Badenoch in the Tory leadership contest last year, will be meeting Vance for the first time in the Cotswolds.
The Tory shadow secretary of state and Vance have taken similar positions on a range of policy issues, from immigration to free speech.
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