The two sides reportedly made verbal promises during the latest round of talks, with only a few details missing.
Arsenal manager Mikel Arteta had hoped winning the FA Cup would convince Aubameyang, the club's captain and leading scorer, to stay.
"Winning a trophy helps to really believe and feel, 'Wow, I want more of these moments,'" Arteta said prior to Arsenal's 2-1 win over Chelsea in the FA Cup final. "If you are wearing the armband and able to lift that cup, it is such a moment. This is going to help for sure."
Aubameyang finished second to Leicester City striker Jamie Vardy in the Premier League scoring race with 22 goals in 36 appearances and scored both goals in the final. He also became the quickest player to reach 50 Premier League goals in club history.
But with just 12 months remaining on his current deal, Arsenal were running the risk of losing Aubameyang on a free transfer. The Gunners were roundly mocked when they allowed midfielder Aaron Ramsey to walk for nothing.
If Aubameyang signs on the dotted line, the club will avoid further embarrassment and signal to its fans they're still willing to invest in the squad.
Law's report comes a day after Arsenal announced they would cut 55 jobs as a result of the coronavirus pandemic, a move that's drawn heavy criticism.