Moyes was among the crowd to see the striker, 16, make his debut for the full national side against Croatia in midweek.
EXCLUSIVE: Lukaku - the teenage star wanted by Chelsea who they call the new Drogba New Drog, old tricks: Teenage prodigy Romelu Lukaku shows his strength, just like Chelsea striker Didier Drogba, playing for his current club Anderlecht
The Anderlecht youngster, dubbed the 'new Didier Drogba' is already on the radar of European football's leading clubs but the Scot wanted to see what all the fuss was about for himself.
Lukaku does not celebrate his 17th birthday until May but already stands at 6ft 2in and would command a hefty price tag should a bidding war start for his services.
VIDEO: The 'next Drogba' in action.
EXCLUSIVE: Chelsea target Lukaku - the sensation they call the new DrogbaVIDEO SPECIAL: Watch footage of Belgian boy wonder Romelu LukakuArsenal keeping an eye on Anderlecht hot-shot teenage striker LukakuEVERTON FC