Lukaku scored a hat-trick against Manchester United on Sunday to finish his first full Premier League campaign with 17 goals for West Brom, and the Baggies are keen to keep him next season.
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"Lukaku has been amazing for West Brom this season and I'd hope that he would prefer to live in London," Sullivan told The Mirror.
"He [Carroll] and Romelu would be devastating. The best strike-force outside of the top six or seven.
"Lukaku would be a loan. We would maybe buy him a year later if Chelsea decide they don't want him."
Meanwhile Lukaku himself admits that, with the managerial situation at Stamford Bridge still to be resolved, he cannot be sure of next year's plans.
"It is out of my hands," he told The Express and Star.
"I will go to the internationals, go on holiday with my friends and my missus and come back and train hard with my dad and then go to pre season with Chelsea."
The 20-year-old has been called up by Belgium for their friendly against USA later this month, alongside eight other Premier League players.