The 2018 World Cup winner has just six months left on his deal at Paris Saint-Germain having so far refused to extend his stay.
It has been widely reported that should he depart France, he would link up with LaLiga leaders Real Madrid.
But according to The Times, a switch to Spain appears uncertain with the 25-year-old unimpressed by Real's attempt to pressure him into signing a pre-contract.
Real are claimed to have imposed a January 15 deadline on Mbappe to agree terms regarding a summer transfer.
And this allegedly has rubbed the ex-Monaco star up the wrong way - telling friends that Real will not decide his future for him.
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As it stands, Mbappe is said to have so far rejected their proposal.
He is now exploring a possible move to the Premier League as he weighs up his future.
Liverpool are known to be admirers of the player, with the Merseyside outfit coming close to signing him in the past.
Mbappe revealed he held talks with the Reds before he linked up with PSG in 2017.
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Meanwhile he has also revealed he almost joined Arsenal. Mikel Arteta known to be in the market of bolstering his attack.
Mbappe was recently asked by French media whether he has made his mind up over where he will be playing next term.
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But he remained coy on his future, as he said: "No. I'm very, very motivated for this year.
"It is very important. As I said, we have got titles to go after and we have already taken one.
"After that, I haven't made up my mind yet. I have not made a choice."
Mbappe has been in lethal form yet again this campaign - chipping in with 22 goals in 23 games in all competitions.