The breakthrough suggests the long-running saga is approaching a happy conclusion for the Gunners but the fact the Bundesliga side will only sanction the completion of the deal once they have secured a replacement could yet prove a stumbling block.
Negotiations have been ongoing for Aubameyang for a fortnight, with Arsenal always confident a deal could be concluded this month after the player made it clear he was keen to move to London.
A three-and-a-half year contract has been agreed with the Gabon forward believed to be worth £180,000-a-week, though reaching a deal with Dortmund has proven a far tougher challenge.
An Arsenal delegation led by the chief executive Ivan Gazidis, and including the new head of recruitment Sven Mislintat and Huss Fahmy, who works on player contracts, spent time in Dortmund last week, with talks having continued in the period since.
Reports in Germany suggest a deal was settled in principle over the weekend for a player who moved to Dortmund in 2013 and has proved prolific, if controversial at times, ever since.
Dortmund have made clear that they must secure a forward replacement for the outgoing Aubameyang before the transfer is formally signed off.
There have been talks with Arsenal over Olivier Giroud but the Frenchman is understood to be reluctant to leave London mid-season and is believed to be more tempted by a move to Premier League rivals Chelsea.
Anthony Modeste, who joined the Chinese Super League club Tianjin Quanjian from Cologne last summer, has been mooted as a potential addition, but would cost around €30m (£26.4m).
Michy Batshuayi, scorer of a brace for Chelsea on Saturday but a player who would be permitted to leave on loan if a replacement is secured before Wednesday’s cut-off, is another option the German club may pursue.
Aubameyang’s addition would be a huge boost for Arsene Wenger after a testing start to January saw the Gunners exit the FA Cup, lose ground in the race for a top four finish and allow Alexis Sanchez join Manchester United.
Things have picked up in recent weeks, Arsenal following a 4-1 Premier League win over Crystal Palace by sealing a place in the Carabao Cup final against Manchester City after a 2-1 aggregate victory over Chelsea.
Arsene Wenger’s men will look to maintain the momentum at Swansea tonight as Petr Cech goes in search of his 200th Premier League clean sheet.
The 35-year-old already holds the record for the number of Premier League clean sheets but has been stuck on 199 for six games.
“I am proud because when I came to the Premier League in 2004 obviously I was 22 years old and you think: ‘Oh wow, this is everything I dreamt about and I am here’,” he said.
“So it was up to me to show I am capable of playing in this league and obviously since I started it all went the direction I wanted and I always wished for.
“I have to say, sometimes when you look back and you speak about coming to 200 clean sheets in the Premier League and you see how many games everybody else needed to get there and nobody ever got that far, you think ‘it is something amazing’ and I hope it is going to go way longer than 200.”
Cech insists he has no plans to consider retirement as the ex-Czech Republic international closes in on his latest landmark.
He will head to Swansea with a pair of drumsticks tucked away in his kit-bag having discovered a passion for playing the drums in recent years.
After forming an impromtu band with former Chelsea goalkeeping colleagues Carlo Cudicini and Hilario, Cech now posts his drumming videos on YouTube — where he has amassed over 2.5 million views.
“I have to confess that in my bag, I always carry a pair of drumsticks because you never know where you find the time to do a little bit,” he said.
“Usually, when we go to an away game, I have a little practice pad and drumsticks with me. If you sit three hours in your hotel room somewhere before you have another activity, you can use it in plenty of different ways.
“I started playing when I was almost 30 years old. Actually, I bought a drum kit in March 2011. That was when I started.
“I have to say it happened by accident because I enjoyed music and always listened to it but Carlo Cudicini plays piano.
“Once, we went out for dinner and we ended up back at his flat with Hilario. He had this Guitar Hero, Playstation setup with a little drum and two guitars. We ended up playing the game just for fun.
“The original thought for putting videos out is to show people that if you enjoy something, no matter what, you can do it.”
Having joined Arsenal in a swap deal for Sanchez, Henrikh Mkhitaryan is set to make his Arsenal debut tonight. The Armenian is relishing his new challenge, particularly working with Wenger.
“Of course it’s very important to have respect from your manager,” said. “I know that he’s demanding and he likes his players to explore. He was one of the reasons to join Arsenal as well because everyone knows he’s a great manager.
“I’ve known him for a long time and of course it was not very difficult to make this decision to come to Arsenal, because I think the way that Arsenal play makes it a dream for every player to come here and play offensive football.”
Swansea boss Carlos Carvalhal has huge respect for Arsenal but insists his side won’t play for a draw. “They have a fantastic squad and coach. They are one of the best teams in England and the world,” Carvalhal said.
“We will have to work very hard and expose their weak points. They have very few, but we will try to exploit it. We will fight to win — we don’t play to draw.”