The Bees see Ouattara as a replacement for Bryan Mbeumo after his sale to Manchester United.
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The need for attacking reinforcements is at a premium for Brentford, with Yoane Wissa also potentially leaving for Newcastle United this week.
The Daily Mail says Ouattara is keen to hear from Brentford as he's open to "exploring" his options this month.
The attacking talent joined Bournemouth from Lorient in 2023 and has made 88 appearances for the Premier League club.