Belgium forward Lukaku left Goodison Park for Manchester United this summer in a £75million deal after scoring 20-plus goals in each of his previous three seasons with the Toffees.
The 24-year-old already has six in as many games for his new club and although Koeman knows his defenders will be fully aware of the threat Lukaku carries, he stressed they must tighten up at the back or they will be undone by a familiar face.
"We know him really well," Koeman said of Lukaku. "He's one of the best strikers.
"I mentioned several times last season he's a great finisher. I hope that we know how we have to defend against him.
"There are a lot of individual qualities in the players around him (at United). In the box he's really dangerous, he's fast, he's strong.
"If we defend how we've defended in the last few games then maybe it will be his afternoon."
The Toffees head for Old Trafford after suffering back-to-back 3-0 defeats and having failed to win any of their last five matches since their opening-day victory over Stoke.