Per Toni Juanmarti at Sport, the Catalan giants would look to purchase him at the end of this season, for his buyout clause of €35 million.
Reus is contracted at Dortmund until 2017, and with what happened to Mario Gotze fresh in the memory, Dortmund want to extend Reus' contract.
Do Barca need Reus?
Gotze signed for Bayern Munich after they shelled out €37 million to pay his release clause and caused a stir among Dortmund supporters.
However, per Bild (h/t David Kent of the Daily Mail), talks over a new deal collapsed and Reus is trying to engineer his way to one of the world's top sides.
However, while turning your nose up at the chance to sign one of the world's biggest stars is not something that many clubs have the chance to do, Barcelona are in a position where the pursuit of Reus would be totally unnecessary.
They have several attacking options, with the front line of Luis Suarez, Neymar and Lionel Messi more than enough firepower and the likes of Andres Iniesta, Gerard Deulofeu, Pedro and Ivan Rakitic able to provide the ammunition.
The only reason Reus needs be pursued is if Iniesta shows a rapid decline in form this season now he has turned 30.
However, if the World Cup is anything to go by, where he comfortably outperformed every other player in a misfiring Spain squad, then a loss of form will not be an issue.
Reus, 25, would be a good long-term replacement for Iniesta, but you have to assume the Spaniard has another two seasons at the top of his game at least.
Furthermore, Messi is more than comfortable dropping deeper and playing in the hole.
Part of the reason for signing Suarez, or any No. 9-type figure, is to have a plan B.
That would be to pull Messi in from the front, so he can pull the strings between the midfield and the attack.
Suarez or Neymar, or even the pair of them, would then spearhead the attack.
Furthermore, if Enrique intends to field Javier Mascherano in midfield, then there's one less role that Reus could feature in.
It has been suggested that the Argentine could play alongside Sergio Busquets as a double pivot at the base of Barcelona's midfield.
Ahead of them this season could be any of Iniesta, Rakitic or pass-master Xavi, who is staying for the final year of his contract.
Perhaps at the end of the season when Xavi goes, you could argue for Reus to replace him.
In reality, Rakitic would like to have made enough of an impact by then to claim that attacking midfield position for himself.
Reus is a fantastic player, of that there is no doubt. But it's time Barcelona looked at the areas they really need to improve on, rather than simply cherry-picking the best attacking talent.