Omur, 25, signed with Hull from Trabzonspor in February last year, making 36 league appearances since his arrival.
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His most recent outing for Ruben Selles’ side came in a 1-0 loss to Middlesbrough on January 1.
Hull currently sit just one point clear of the Championship relegation zone but have a game in hand over 22nd-placed Derby.
The Turkish international will aim to regain form and regular minutes during his stint with Rizespor.