Only bottom side Blackpool with 91 goals conceded last season had a leakier defence than Fulham, who let in 83 over the course of the campaign.
And the Whites have, allegedly, made a bid for the Bees defender, who helped Brentford reach the Championship play-offs.
Despite some high-profile errors towards the end of last season, Tarkowski, who signed from Oldham in January 2014, is highly rated by the hierarchy at Griffin Park and it expected they would look for closer to £3m for their prized defender.
Since joining the club, the 22-year-old has made 47 league appearances for the Bees and scored three goals.
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