The 22-year-old defensive midfielder has been heavily linked with a move away from Monaco at the end of the season and he is expected to be in demand in the summer.
Chelsea and Manchester United have been tracking him with a view to potentially signing him in the summer transfer window.
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Real Madrid are also big admirers of the defensive midfielder and are keen to lay their hands on him in the coming months.
But it has been claimed that Real Madrid are wary of the financial demands being made by Monaco at the moment.
Real Madrid are interested in Tchouameni but do not want to pay through the roof to sign him.
For the moment, Real Madrid will not be adhering to the demands of Monaco in their pursuit of the midfielder.
They are waiting for Monaco to reconsider their financial expectations before tabling an offer for him.
Barcelona are also interested in getting their hands on him and are tracking his situation at Monaco.