The 22-year-old was a shining light for CSKA Moscow this season and he has been tipped to star at the World Cup.
Arsenal are already tracking the midfielder closely with a view to a bid this summer.
But, according to RMC, Monaco have expressed an interest in Golovin and are trying to hijack Arsenal’s offer.
The French club have kicked off talks with the Russian’s representatives and they want a deal done before the World Cup.