Meredith has played 26 games for Bradford so far this season.
The Australia international has helped the Bantams up to fourth in the League One table.
Leeds are on the lookout for a full-back to replace Charlie Taylor.
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James Meredith has been at Bradford since 2012
Taylor could leave this month with several Premier League sides said to be interested in him.
The player’s current deal expires at the end of the season and Taylor wants a move away from Elland Road.
And the Daily Star claim Leeds’ search for a defender has led them to Meredith.
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Charlie Taylor is expected to leave Leeds
Chris Wood scores with stunning overhead kick for Leeds
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The 28-year-old’s contract expires in the summer and Whites boss Garry Monk is preparing a £350,000 bid to land his man this month.
Norwich are also interested in signing Meredith after selling Martin Olsson to Swansea.
However, despite Leeds flying high in third in the Championship table, Meredith could stay at Bradford to help boost their own chances of securing promotion.