According to unnamed Belgian sources cited by talkSPORT, the wealthy Ligue 1 outfit have joined the race to sign the Standard Liege striker and dispatched scouts to run their eye over Batshuayi during Friday's clash against Zulte Waregem.
20-year-old Batshuayi - who moved to his current employers in 2008 - has been in impressive form this season, notching 18 goals in 31 appearances for Guy Luzon's Pro League leaders.
Such scintilating displays at Stade Maurice Dufrasne have seen Premier League transfer interest in the Belgium U21 starlet develop quickly in recent months, with out-of-form Arsenal having been linked with Batshuayi as well as fierce North London rivals Tottenham.
Both clubs - who have each endured difficult spells of late - must surely be considering moves for forward reinforcements this summer.
With the disappointing Nicklas Bendtner set to depart the Emirates Stadium upon the expiration of his contract, Arsene Wenger will be left with just Yaya Sanogo as the only back-up option to compatriot Olivier Giroud.
Tottenham, meanwhile, lavished a then club-record fee to bring Spanish striker Roberto Soldado to White Hart Lane last summer, but are yet to see a significant and worthwhile return from the former Valencia man.
And while Emmanuel Adebayor has shown signs of improvement since Tim Sherwood replaced Andre Villas-Boas in the managerial dugout in December, it seems very unlikely that he will continue in the role beyond the end of the season.
However, if either Arsenal or Tottenham have serious hopes of landing Batshuayi, it appears as if they will have to act fast with Monaco circling and presumably well capable of matching the player's £6.5 million release clause.