The series finale is to be held in Headingley on Tuesday.
The 27-year-old batsman Vince has been called up for the Leeds game.
For Hampshire, he scored 109 versus Somerset and 171 against Yorkshire in England's domestic one-day tournament. It is unlikely he will feature in the playing eleven on Tuesday, though.
Squad: Eoin Morgan (captain), Jason Roy, Jonny Bairstow, Jos Buttler, Moeen Ali, Joe Root, Jake Ball, Liam Plunkett, Ben Stokes, Adil Rashid, David Willey, Mark Wood, James Vince.
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