Sinclair, 18, signed his first professional deal in the summer after making his debut in the EFL Trophy last season.
He was the club’s academy player of the year, and started for Radcliffe in the 1-0 defeat at Basford United on Saturday.
The club have also signed defender Javid Swaby-Neavin on loan from Oldham.
Swaby-Neavin, 18, spent last season with Ashton United before joining the Latics, and will be at the Neuven Stadium until the New Year.
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