The Bees are eager to sign a centre forward, per The Sun, as they close in on the sale of Ivan Toney.
The forward wants to leave for a Champions League club, while Brentford will not stand in his way.
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The 24-year-old Sargent, who has played in the Premier League, has impressed for the Seagulls.
He has managed 11 goals in 17 matches this term, while Brentford believe he can improve.
Norwich are seventh in the Championship and will only be able to hold onto Sargent if they gain promotion.