Bowman tore the ACL and MCL in his left knee during last season's NFC Championship Game against the Seattle Seahawks. He underwent surgery on Feb. 4.
Bowman is on the physically unable to perform list, meaning that if the 49ers clear him to return to practice, they'll have 21 days to decide whether to activate him or send him to IR.
"He has been doing some cutting; and he's cutting pretty darn well," Harbaugh said. "(Tuesday) will be a big day."
The 49ers have also been without fourth-year veteran Aldon Smith, who is expected to make his season debut Sunday against the New York Giants after serving a nine-game NFL suspension for personal conduct policy and substance-abuse policy violations.
Rookie linebacker Chris Borland led San Francisco in tackles in each of the past three games. Michael Wilhoite and Dan Skuta have also combined for 65 tackles as part of the group helping veteran Ahmad Brooks.
Harbaugh said he will be pleased to have the 49ers' linebacker unit return to full strength.
"It's a position of depth and strength," Harbaugh said. "It's always been that, guys have always played to a high standard there. ... It is a position of strength, and we'll keep trying to build on that."
- Mike Fiammetta