The 29-year-old was on the bench for his side's first three matches of the 2021-22 Premier League season but missed out against Liverpool last weekend due to a calf strain.
The issue will force the experienced midfielder to miss Friday's league encounter with Newcastle United, but Bielsa has said that Forshaw is in line to face Fulham in the EFL Cup on September 21.
The Englishman featured in the last round of the League Cup, playing 61 minutes of the 3-0 home success over Crewe Alexandra towards the end of August.
"Adam Forshaw is finishing the recovery of his injury and from next week he will be available," Bielsa told reporters during his press conference on Thursday.
Forshaw's future at Elland Road is unclear, as his current deal is due to expire next June. body check tags ::