The defender remains unavailable for selection ahead of their UEFA Champions League league-phase trip to Paris Saint-Germain on Tuesday night.
The 24-year-old Japan international took part in Monday's final session at Sabener Strasse but will not be named in the matchday squad for the first time this campaign, according to the latest team news.
His progress nonetheless offers a timely defensive boost for coach Vincent Kompany as Bayern prepare for one of their toughest away fixtures in Europe.
Kompany confirmed that only long-term absentees Jamal Musiala (leg) and Alphonso Davies (ACL) remain sidelined. The Belgian, whose contract was recently extended until 2029, expressed optimism about the squad's overall fitness ahead of the clash.
Ito joined Bayern from VfB Stuttgart in the summer of 2024 and was expected to play a key role before his injury setback, a recurrence of a preseason issue that required surgery and sidelined him for most of the campaign so far. His ongoing recovery strengthens Bayern's defensive options as they look to build momentum in the revamped league phase.
Bayern have made an unbeaten start in this season's Champions League, winning all three of their opening matches, and will travel to the Parc des Princes aiming to extend that run.
PSG, the defending European champions, share the same perfect record after three wins and will look to make home advantage count in what promises to be a high-tempo encounter between the top two teams in the standings.
Kick-off in Paris is scheduled for 22:00.
Mikel Arteta has admitted Arsenal must remain grounded despite their stunning start to the season, as the Gunners continue to battle on multiple fronts at home and in Europe.
Tottenham manager Thomas Frank has eased fears over injuries to Mohammed Kudus and Djed Spence ahead of Tuesday's crucial Champions League clash with Copenhagen.
Real Madrid have been dealt a major setback ahead of their Champions League trip to Liverpool, with teenager Franco Mastantuono ruled out through injury.
Luis Enrique has said Paris Saint-Germain are confident they can end Bayern Munich's remarkable 15-match winning run in the Champions League when the sides meet at the Parc des Princes on Tuesday night.
