The 22-year-old is reportedly delaying contract negotiations.
Cortouis's Belgium team-mate traded Stamford Bridge for Goodison Park in a £28 million move this summer, as Jose Mourinho failed to give him guarantees that he would be a first-team starter for the Blues.
Lukaku had previously spent season-long loans at West Brom and Everton and returned to west London this summer with the knowledge that Chelsea had forked out £32m on new forward Diego Costa.
The Standard claim that the Blues offered Lukaku a five-year deal this summer, with another loan move on the horizon this term.
However, the Belgian rejected the deal and instead joined Everton - and Courtois is reportedly fearful of a similar fate.
The 22-year-old faces a battle for the no.1 shirt at Stamford Bridge with Petr Cech, while Mark Schwarzer is also a backup option at Chelsea.
Once Courtois learns his true status within the squad, he may be more tempted to negotiate with the club - especially if he is indeed unveiled Mourinho's first choice.
Should Cech be given the nod ahead of the Belgian, though, Courtois's future would become less certain.