The 30-year-old has been an important part of the Whites midfield in recent months in the Premier League following his return to playing regular football.
Forshaw spent nearly two years sidelined due to a complex hip problem that required a number of surgeries and a lengthy rehab process.
He missed the majority of United's Championship promotion campaign along with the club's entire debut season back in the top flight after 16 years away.
Forshaw, though, has been in strong form since playing week in, week out once again.
He has had to take on added importance too - starting the last eight games in a row under Bielsa - following injury to Kalvin Phillips early last month that has seen the England international ruled out until March.
The central midfielder is out of contact in the summer and is proving his worth to the Elland Road outfit with a decision looming on his future.
"The extension of Forshaw’s contract is something between Forshaw and the institution. Clearly, his return to the team has been satisfactory," Bielsa said ahead of this weekend's clash against Burnley in LS11.
"When he’s played as a defensive midfielder, or as a box-to-box midfielder, he’s offered solutions. The absence of [Kalvin] Phillips he has helped to resolve with Pascal [Struijk] and [Robin] Koch.
"He’s offered options that were very necessary in the number 8 position with [Mateusz] Klich and [Stuart] Dallas. His level of performance is the same as that prior to the injury. Prior to him stopping playing, he was at a very good level.
"Two years later, he has been able to play at a very high level at a higher level of competition - that is not common. The club has supported him, and he made big efforts to be able to get back to this level and I am sure that he is enjoying it."