The 24 year-old defender is attracting interest from the Premier League's biggest clubs before the September 1 deadline.
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The Daily Mail says Manchester United, Liverpool and Tottenham are all targeting Collins as they seek a new centre-half addition.
The Republic of Ireland international was named Bees captain this summer after the sale of Christian Norgaard to Arsenal.
Before moving to Brentford, Collins wore the captain's armband at 18 with Stoke City.
The defender has a deal with the Bees to 2029.