The 19-year-old has worked his way into the first-team under manager Marco Silva at the start of the season.
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The England U18 international has a contract with Fulham until 2022, meaning that he could well have his pick of a number of clubs next summer.
And Crossley believes that a number of Premier League clubs will want to bring the teenager in, and has urged Fulham to stay near the top of the table in a bid to ensure he stays.
Fulham are currently top of the Championship, having taken 13 points from their opening five games.
Speaking exclusively to This Is Futbol, Crossley said: “If Marco Silva’s picking him, and he’s playing regularly, such a young lad… I haven’t seen too much of him but what I have seen, Fulham have to stay at the top of the league because Premier League clubs are going to be all over him at this moment in time.”