The Catalan outfit have been busy in the current market, adding Andreas Christensen, Franck Kessie, Raphinha, Robert Lewandowski and Jules Kounde to their squad.
However, head coach Xavi is still believed to be determined to improve his options at full-back, with a new right-back and left-back wanted before the end of the transfer window.
According to Marca, Barcelona have another €57m (£48m) available to spend before the market closes, but they do not have any space in their wage budget to bring in new players.
The report claims that a departure for Aubameyang would solve the issue, though, and allow the team to bring in a new right-back and left-back before the window slams shut.
Aubameyang has lost his starting role at Barcelona this season to Lewandowski, and Chelsea are believed to be keen to bring him back to the Premier League.
There have also been suggestions of interest from Manchester United, with the Red Devils potentially allowing Cristiano Ronaldo to leave in the latter stages of the window.
Barcelona have been linked with Villarreal's Juan Foyth, Borussia Dortmund's Thomas Meunier and Arsenal's Hector Bellerin in their bid to sign a right-back.
However, a recent report claimed that the club are currently in talks with Rennes over a deal for Hamari Traore, with the 30-year-old potentially available for as little as €3m (£2.5m), as his contract is due to expire next June.
Chelsea's Marcos Alonso continues to be linked with the club as a possible left-back addition, although Celta Vigo's Javi Galan is also allegedly being considered.
Speaking during Saturday's press conference, Barcelona boss Xavi also said that he was still "hopeful" of signing Bernardo Silva from Manchester City before the deadline.
"I am hopeful, of course. But we know it is going to be difficult because there are only a few days left and with the current situation I see it as really difficult," Xavi told reporters.
A deal for the Portugal international is only allegedly a possibility if Aubameyang, Memphis Depay, Frenkie de Jong, Sergino Dest and Martin Braithwaite all leave before the transfer deadline.
The speculation surrounding De Jong's future has quietened in recent days, though, with Manchester United believed to have dropped their interest.
Memphis has also seen a move to Juventus break down, while Dest and Braithwaite are seemingly holding firm at Camp Nou despite being informed that they are not in the club's plans moving forward.