Flick revealed last month that he will leave the Allianz Arena at the end of the campaign, bringing down the curtain on a trophy-laden two-season spell in charge.
The 56-year-old is the strong favourite to take over from Joachim Low as Germany's next boss when the latter steps down after this summer's rearranged Euro 2020 tournament.
However, ESPN claims that, with no agreement yet believed to be in place between Flick and Germany, Barca could be about to pounce.
It is suggested that the Catalan giants have already reached out to the German's representatives, with president Joan Laporta a big fan of his coaching methods.
Koeman has only spent one season at the Camp Nou helm and has another year to run on his deal, but Barca have endured a disappointing 2020-21 campaign.