According to AFP (h/t Wally Downes Jr. of the Sun), the Gunners have offered £44.6 million for the forward, but the German said: "I can’t imagine for one moment Aubameyang leaving. He is the core of the team. We have a lot still to achieve with him. There is no debate about it."
The African Player of the Year has also been warned against moving by BVB chief executive Hans-Joachim Watzke.
He told German newspaper Bild (h/t Rob Burnett of the Mirror): "The players are squeezed there, often like a lemon. They are given hardly any rhythm in their game. Professionals who reflect on something more than just what arrives at the end of the month in their pursue [sic] will take this into account when making a decision."
Aubameyang has reportedly caught Arsenal's attention following his incredible exploits this season, in which he has netted 27 times in as many games and assisted a further six.
With Olivier Giroud in good form, the Gunners have been fairly strong up front in this campaign—though they have been outscored by Leicester City, Manchester City and Everton thus far, and the likes of Theo Walcott, Alexis Sanchez and Danny Welbeck have all suffered injuries, so another goalscorer would be a useful addition.
Aubameyang is a top-quality performer who would be a brilliant acquisition for any side and could make a huge difference to Arsenal's chances of clinching the Premier League title, but it's highly unlikely he'll be moving in January.
A cheaper alternative could be Celta Vigo's Nolito. According to Javier Gascon of Spanish outlet Mundo Deportivo (h/t Metro's Mark Brus), the Gunners are "ready to pay" his £13.4 million release clause.
The Spaniard impressed last season, with 13 goals and 14 assists in all competitions, and he has firmly maintained his good form with eight and five, respectively, in 15 appearances this campaign.
His form over the last two seasons has seen him break into Spain's national team, and football journalists Dermot Corrigan and Rik Sharma thought he fit right in at international level when he played for La Roja in November:
Dermot Corrigan @dermotmcorrigan
Nolito looks at home at this level.2015-11-13 21:01:30
Rik Sharma @riksharma_
Nolito is so good. Rampaging down the left for Spain2015-11-13 21:01:41
Though he's not an out-and-out centre-forward, Nolito has proved to be a fairly prolific goalscorer from wide positions, and his ability to create for his team-mates would see him fit in well with the Gunners.
As the report notes, though, he is hoping for a move to former club Barcelona. Arsenal would undoubtedly be a tempting prospect for the forward, but his desire to return to the Camp Nou could be such that he's willing to wait for that to materialise.
With their annual injury crisis firmly under way and the Premier League title hanging in the balance, Arsenal can ill afford to sell any players in January.
Nevertheless, according to Hector Andreu of Spanish outlet Fichajes (h/t Metro's George Bellshaw), West Ham United are hoping to recruit Mikel Arteta, as Arsenal will not be offering him a new deal in the summer.
The 33-year-old is largely a squad player at the Emirates Stadium now and has played for just 391 minutes this season due to injury problems. Football tactics expert Michael Cox believes the Gunners were right to keep him in the summer, though:
Michael Cox @Zonal_Marking
@62_tom I think getting rid of Arteta would have been ludicrous, personally, and I think Flamini is a good third-choice holding midfielder2015-12-4 18:26:43
The Hammers' interest presents something of a dilemma to Arsenal, as Arteta could yet prove a useful player in the long campaign ahead, but equally if they don't plan to renew his deal in the summer—an understandable decision given he will be 34 by then—January represents their last opportunity to cash in on the midfielder.