The Germany international has been out of action after breaking his leg during a skiing holiday in December 2022 following their World Cup first-round exit.
He could be ready for Saturday, with reports saying the club's medical team had given the green light for him to return to action.
Bayern, who have not commented on the matter yet, have relied on experienced reserve keeper Sven Ulreich this year and also signed 23-year-old Israeli Daniel Peretz in August.
Ulreich has helped them to three clean sheets in the league this season, the last time they achieved that in the first seven matches of a season was in 2017.
Neuer is not the only player back from injury though with Serge Gnabry, who suffered a fracture in his arm, back in team training this week along with fit-again defender Matthijs de Ligt.
The Bavarians have yet to lose in the Bundesliga this term and, despite being third on 17 points, two off leaders Bayer Leverkusen, are in fine form.
With 23 goals so far they boast the best attack in the league, with winger Leroy Sane having netted six times.
The Germany forward is in superb form, having already scored more goals than he had ever done in the entire first half of a Bundesliga season.
Sane will come up against the joint-worst backline in the league with Mainz having conceded 19 goals.
League leaders Leverkusen, who are also unbeaten following their best start in years, travel to seventh-placed Vfl Wolfsburg hoping to stretch their winning run to four matches.
Xabi Alonso's team have been the surprise of the season so far with their attacking game exciting fans and players such as forward Victor Boniface, with seven goals, already attracting the attention of major European clubs as is the coach himself.
Second-placed VfB Stuttgart, with the league's top scorer Serhou Guirassy having already bagged an impressive 13 goals so far, travel to Champions League side Union Berlin, who have lost their last seven matches in all competitions.
Stuttgart have 18 points, one behind Leverkusen, after six wins and one defeat.
Last year's runners-up Borussia Dortmund, unbeaten on 17 points along with Bayern, can provisionally take over top spot on Friday if they beat lowly visitors Werder Bremen.
