United signed 21-year-old forward Brown on a season-long loan at the end of August but the former England under-20s player arrived on the recovery trail after tearing his anterior cruciate knee ligament whilst on loan at Brighton back in January.
Brown revealed on social media on October 24 that his rehab was going well - saying "not long now" - and Bielsa provided an update as to when Brown might feature at Friday's pre-Wigan Athletic press conference.
Bielsa feels it will be January by the time the Chelsea loanee is ready to compete for a place in his first team.
"The fact that he will be able to come back soon inside the group is less important than to know when he will be able to play with the first-team," said Bielsa.
"And I think he will be able to compete in the beginning of next year."
There is no option to buy as part of the loan deal and Leeds will not pay Chelsea anything until Brown starts playing games.