Bayern Munich have not ruled out making further signings this summer, while new coach Carlo Ancelotti hinted that Mario Gotze and Medhi Benatia may leave.
Bayern have already brought in Germany centre-back Mats Hummels and Portugal midfielder Renato Sanches as they prepare for their first campaign under Ancelotti.
Bayern CEO Karl-Heinz Rummenigge, though, said the Bundesliga champions are open to further reinforcements if the circumstances are right.
"We have already made two strong reinforcements," Rummenigge said at Ancelotti's presentation. "You could see that at the Euro, but I would not shut the door for new players coming in. The transfer market is still open until Aug. 31."
Rummenigge cited the example of the 2014 window, when Javi Martinez sustained a knee injury in the Supercup and Bayern signed Benatia from Roma to provide cover in defence.
He added: "The sea is calm, I would say. I won't rule anything out."
Benatia has been linked with a return to Serie A this summer, with Juventus reported to be leading the race for his services.
Ancelotti said: "I think the squad is really good, but I have to speak with Benatia. I don't know what's happening with him."
Gotze, meanwhile, has entered the final year of his contract at Bayern and, while he vowed to fight for his place in May, Rummenigge subsequently made clear that the attacking midfielder was not in the club's plans.
Asked about the Germany international, Ancelotti said: "I say what I said about Benatia -- I will treat him as a Bayern player. I spoke with him a month ago, but this is a private conversation. He is a Bayern player, and I don't have to think other things."
The Daily Mirror has reported that Borussia Dortmund are set to re-sign Gotze despite interest from Tottenham Hotspur.
Bayern midfielder Pierre-Emile Hojbjerg is also set to join Southampton, with Rummenigge saying: "Hojbjerg has gone for a medical at Southampton today."