Vinicius Jr went off injured midway through the first half of the 1-0 victory over Celta Vigo on 25 August.
The Brazilian has been out of action since then, and was also ruled out of international duty.
Tests had confirmed that he had damaged his right hamstring.
The Brazilian was initially ruled out for at least six weeks, but that may no longer be the case.
Reports by Marca claim that Vinicius Jr is working hard behind the scenes to speed up his return from a hamstring injury and make it back on to the pitch ahead of schedule.
There is said to be growing optimism that Vinicius could be back sooner than expected.
Vinicius have been having regular scans since the injury, and reports say that Vinicius will be back in no time. However, the club has no plans to rush him.