The pair held either end of the flag during a lap of honour and Choudhury had it draped over his shoulders when he collected his medal following the 1-0 victory over Chelsea at Wembley.
The move came amid renewed conflict between Israel and Palestine, and was interpreted in some quarters as a political gesture.
However, it is understood the Football Association does not investigate the general use of flags on the field of play.
Fofana was one of the stand-out performers for the Foxes at Wembley, while Choudhury made a late appearance as substitute.
Additional reporting by PA
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