The 19-year-old has joined the Barclays Premier League club on loan and is scheduled to play for their academy side against Aston Villa on Saturday.
"Fulham were looking for a keeper for their Under-19s and have invited Ryan down for the week as an experience, and then we will see what develops," Vale assistant manager Mark Grew told the club's official website.
Boot, who signed a two-year professional contract at the Sky Bet League Two club this summer, was brought to Vale Park after being released by city rivals Stoke three years ago.
He is highly thought of at Vale but has yet to make a first-team appearance for the club and finds himself behind Chris Neal and Sam Johnson in the pecking order.
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