Sky Sports reports that the French defender is becoming increasingly unsettled at Leicester due to the situation.
Fofana, 21, wants to play in the Champions League to increase his chances of being picked for France at the World Cup this winter.
The Foxes have so far rejected two bids from Chelsea in the region of £60m.
Leicester is said to want more than the £80m they received for Harry Maguire.
But that rationale is said to be frustrating Fofana due to the differences between them and their careers to date.