The Germany international is in the final year of his Barcelona contract, having joined from Manchester City in 2023.
Gundogan is one of the top earners at the club, and Spanish media reports suggested he might leave after the signing of midfielder Dani Olmo.
Gundogan missed Barcelona's opening league match, a 2-1 win at Valencia on Saturday due to a minor injury. "(Gundogan) hurt his eyebrow on Monday and that's why he's staying at home," Flick told reporters after the game.
"I appreciate what kind of player he is and what he is like as a person. I've talked to him a lot, but it's something between me and him, we have a good relationship. I know him well. I have the feeling that he will stay."
Barcelona host Athletic Bilbao next in La Liga on Saturday.
