The Sun says the Bees want competition for David Raya and like experienced Flekken, 29, who is at German side Freiburg.
Brentford have allowed Alvaro Fernandez to return to Huesca after his season-long loan. Jonas Lossl was also on-loan from FC Midtjylland.
Flekken kept ten clean sheets in 32 Bundesliga appearances in the most recent campaign.
The Holland international is rated at £10m by Freiburg.
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