The team was named recently by the FIA alongside Red Bull Racing and Williams as having failed to fully comply with the 2021 financial regulations.
However while Red Bull was deemed to have overspent and made procedural errors, Aston Martin and Williams were only guilty of the latter.
The Williams case, involving the late submission of documents by a third-party accounting firm, was settled with a $25,000 fine earlier this year.
Aston Martin has been in negotiation with the FIA for some time, and a result is likely to emerge this week.
An ABA means that the team admits that it was wrong and formally accepts any penalty applied by the governing body.
"We are in discussion with the FIA," said team boss Mike Krack when asked about the situation by Motorsport.com.
"I think it will be something that we try to conclude in the next days. So we had some discussions over the weekend as well with them. And I'm quite confident that we'll get it solved soon."
Krack played down the suggestion that there was any frustration in the camp about PR damage done by being associated with wrongdoing.
"I think it's complex, it's a complex set of regulations," he said. "And it is not frustrating, it shows us that we have to do a better job in the future, that we are not having such issues.
"But at the end of the day, I think probably the most important thing is that we were under the cap. And the rest is procedural."
The Aston breach is believed to be associated with a tax issue that was specific to the UK, and which was interpreted in different ways by the team and the FIA. However, Krack declined to give say anything on the matter.
"I would prefer that we have a signed agreement before we can go into it," he said. "There will also be a press release, I think from the FIA, that is then agreed with us. So there will be more details in the coming days."
Krack said he doesn't know when any news might emerge from the FIA, but indicated that the Aston outcome won't necessarily have to wait for the Red Bull case to be resolved.
Talks between the Milton Keynes team and the FIA were put on hold after the death of Dietrich Mateschitz.
"I understood from reading [the media] that they postponed, because of Dietrich Mateschitz," said Krack. "Actually, they are two independent things. So I would not mind that we finish ours as quickly as possible. And also, it's a different situation, we are not overspending.
"It depends also on the FIA. And then now we have people travelling, but I think we did a couple of steps this weekend. So I think we're not far. But I cannot tell you if it's tomorrow, or Wednesday or whatever."
