The 21-year-old, who hit 15 Premier League goals while on loan at Everton last season, has an uncertain future as it remains unclear whether he is involved in Jose Mourinho’s plans at Stamford Bridge.
Chelsea already look set to boost their striking options this summer, with Diego Costa understood to have passed a medical ahead of a proposed move from Atletico Madrid.
Lukaku is currently at the World Cup in Brazil with Belgium and he has already conceded that he may need to depart the club in order to continue playing regular football.
Allofs has previously confirmed the Bundesliga side’s interest in a move for Lukaku as they chase a new striker, but he knows that they may face stern competition to secure his services with a host of Premier League clubs, Juventus and Atletico among those also reported to be keen.
"If the player is getting cheaper, maybe this affair is picking up pace. But even then we won’t be the only club chasing the player’s signature," he told kicker-Sportmagazin.
"Actually we are looking at top-class strikers and we do not have any pressure. We are patiently waiting for the right moment.
"There will be some movement in all of this after FIFA World Cup tournament."