The Belgian international spent last season on loan at Goodison Park, netting 15 Premier League goals.
This form has led to talk that the Toffees and Spurs are looking at taking him from Chelsea on a permanent basis, but now Dortmund are also in the battle.
The Bundesliga giants are thought to be readying a £20m offer for the youngster.
Jose Mourinho is believed to be against welcoming back Lukaku for next season, with the pair rumoured to have a less than fruitful relationship.
Although they are willing to sell to a domestic rival, an offer from Dortmund may be more tempting.
With Diego Costa set to sign for Chelsea, Lukaku is seen as expendable which has alerted Dortmund.
The 21-year-old is seen as a direct replacement for Robert Lewandowski, who will be a Bayern Munich player next season after agreeing a Bosman switch to the Allianz Arena.