Niko Kovac has confirmed Lucas Hernandez has undergone successful surgery on his knee injury and should be fit for the start of the 2019-20 season.
The France defender, who can play at left-back or centre-back, was announced as an €80 million (£68m/$90m) signing from Atletico Madrid on Wednesday after Bayern triggered his buyout clause to smash the Bundesliga's transfer record.
Lucas will not play again for the La Liga side as he went under the knife to resolve damage to the medial collateral ligament of his right knee.
The 23-year-old will undergo rehabilitation in Germany under the watch of chief medical officer Dr Hans-Wilhelm Muller-Wohlfahrt but Kovac cannot guarantee Lucas will be ready for pre-season.
"Dr Muller-Wohlfahrt is in contact with the surgeon," Kovac told a news conference on Thursday.
"And if everything goes well, then he should be fit for matchday one. That does not mean that he will inevitably be [ready] on the first day of training.
"He is a world champion and is young, he can take many different positions, he will certainly strengthen us.
"He was operated on yesterday, that sounds weird, but our doctors thought that the surgery was very, very good.
"He will do the rehab under the supervision of our physios and in consultation with Atletico here in Munich."
Robben is set to leave Bayern at the end of the season and Kovac is unclear when the 35-year-old could return.
"It's difficult, I tried once to name a date, but I was wrong, so I cannot say it," Kovac said of the Dutch winger.
"Because at the moment he does not feel that he can participate in team training, or even play games.
"We still have eight Bundesliga games and could play three cup games, I would like him to be able to play not just one or two, but also several games.
"Everything depends on health and you cannot always control everything."