PSV Eindhoven do not want to let Bakayoko go and the winger is not planning on leaving the Dutch giants this summer.
However, the situation could change if the offers grow large enough and Bakayoko has serious interest.
In the Premier League, West Ham are keen, while Everton are claimed to be ready to make an official approach for Bakayoko; Burnley are also suitors.
And the scrap could be a fierce one as, according to Dutch magazine Voetbal International, those around Bakayoko have insisted that more and more renowned clubs from across Europe are touching base.
They are looking to see exactly what it would take for the 20-year-old to move.
PSV Eindhoven would like to keep Bakayoko, but could be tempted to cash in on a player that has yet to fulfil his potential.
It has been suggested some clubs are worried if they wait for Bakayoko to continue to develop then he will become even more expensive in the future.