According to a report by Bild, Dortmund will exercise the option to purchase the striker for €23 million after being given the go ahead by Alcacer.
The former Valencia forward spent two seasons at Barcelona but found game time had to come by with the intense competitions for places.
He made the loan love to Dortmund this summer and has enjoyed a fine start to life in the Bundesliga.
The Spaniard has already banged in seven goals in four games for the club including a hat-trick against Augsburg in his side’s most recent Bundesliga clash.
The striker continued his prolific form on international duty with Spain too, chipping in with two goals in the clash against Wales on Thursday.
In two seasons with Barcelona, Alcacer scored 15 goals across 50 appearances. He recently spoke about his unhappiness at the Catalan club.
“I decided to look for minutes away from Barcelona. After having two years with Barcelona and not playing an important role, not everything went as I’d hoped,” the 25-year-old had told Marca.
“I’m happy now, in the end it comes down to decision making.”
Alcacer’s permanent deal with Dortmund could reportedly tie the striker down to the club until 2023.
The 19-year-old Dutch international has been on Barca’s radar for a long time, having consolidated his spot as Ajax’s starting centre-back during the 2016/17 season, which culminated with an appearance in the Europa League final against Manchester United.
De Ligt has reportedly already informed the Catalan club of his desire to join them, and the club are said to be equally impressed by the young Dutchman.
Midfielder Frenkie de Jong, De Ligt’s team-mate for both club and country, has also been a long-term target for Barcelona. But the club are said to be prioritising signing the defender, given Gerard Pique’s struggles to start this season.
De Ligt is represented by Mino Raiola, who is also the agent of rumoured Barca target Paul Pogba, and the controversial figure will be central in any transfer negotiations between Ajax and the La Liga champions.
The market for centre-backs has also been inflated by the transfer of De Ligt’s fellow Dutch defender, for whom Liverpool paid Southampton £75 million in January, and the price may become a sticking point for Barcelona.
However, their need for defensive reinforcements may force their hand.
The midfielder has been intensely linked with a move to Barca since the summer thanks to a year that has seen him break through with Ajax and the Netherlands.
His graceful and precise style of play has earned him comparisons with the likes of Andres Iniesta and, with the Barca great having moved onto Japanese pastures, it’s a good time for any potential successor.
However, 21-year-old De Jong is in no rush to leave the club that nurtured him – and is a little tired of all the hype.
“In the beginning it was fun and I felt very flattered by the stories around Barcelona, but after a while the questions about it got annoying,” he told ELF Voetbal.
“For the time being, I just stay with Ajax, at least another year and maybe two or three more years. I’m really enjoying myself here.”