Purver, 21, featured in 21 league games during an earlier loan spell this season, scoring twice.
Right-back Michael Taylor, 19, has captained United's under-18 side.
Guiseley are 16th in the National League with seven games remaining this season, seven points above the relegation zone.
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Leeds United pair Alex Purver and Michael Taylor have joined National League Guiseley on loan until the end of the season.