He is yet to commit to fresh terms with the German champions and has entered the final 12 months of his current contract.
That is putting Bayern in a difficult situation, with Flick conceding that Thiago appears ready to take on a new challenge in English football.
He told Sport1: “I can understand when a player is concerned.
“If he wants to try again in the Premier League now, I totally understand. But it would be a shame because Thiago gives our game that certain something.
“That's why I would like, as a coach, to have him on the team for the next few years, but that's life. It would go on.”
No deal for Thiago will be struck any time soon, as he remains part of Bayern’s bid for Champions League glory in 2019-20.
He has already added another Bundesliga title and DFB-Pokal crown to his collection this term.
Pressed on whether a treble triumph would be the perfect send-off for Thiago, Flick added: “I have this feeling with every single member of the team.
“After the double, everyone is really motivated to do everything they can again in the next few weeks.”
Flick’s sole focus at present is locked on a European quest and attention will only be diverted to further transfer matters, and the pursuit of a possible replacement for Thiago, once continental action comes to a close.
“I'll discuss the squad planning with Hasan Salihamidzic and his team. We are in close contact,” said Flick, who has already tied up a deal to bring Germany international Leroy Sane back to his homeland from Manchester City.
“Currently the focus is only on the Champions League.”