Real Madrid are said to be willing to spend a whopping £117MILLION to sign Mbappe ahead of Arsenal.
Express Sport understands Arsenal have had an £87m bid rejected by Monaco.
The Gunners are now considering upping their offer ahead of a second bid.
But reports in France suggest Arsene Wenger's top transfer target is more likely to head to Spain.
According to French radio station RMC, Real are planning the £117m (€135m) deal after TWICE being snubbed by Monaco.
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The Ligue 1 champions are determined not to sell their 18-year-old sensation.
It is claimed Real also had an £87m bid rejected but then saw an improved £95m proposal waved away.
Real have cash to spend, with president Florentino Perez determined to sign a big-name player this summer.
But they will have to raise some cash to ensure they get Mbappe.
It is claimed James Rodriguez will be offloaded and Real Madrid believe they can get £61m for their unwanted playmaker.
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Real Madrid are willing to bid £117m for Kylian Mbappe
Arsenal are also keen to sign Kylian Mbappe this summer
Monaco hope Kylian Mbappe (left) stays for next season
Manchester United are keen on Rodriguez but RMC suggest Inter Milan may also make a move for the 25-year-old.
A source told the radio station: "At the moment, the player wants to stay at AS Monaco, and the club and Mbappe want to continue the adventure."
Staying at Monaco has its advantages for both club and player. Mbappe is seeking a place in the France side for the 2018 World Cup next summer and another stellar season in Ligue 1 would practically guarantee he is on the plane to Russia.
And he would get a mega pay rise if he did stay in Monte Carlo, who Monaco willing to offer him a new contract.