Dennis Wise has opened the bidding with an offer that could be worth more than £250k to the Saddlers if all of the clauses are invoked.
But Walsall have dismissing the first bid out of hand to signal their determination not to have their best young players cherry-picked in the transfer window.
They are now waiting to see whether whether the Whites return to test their resolve further with an improved package.
Leeds are likely to return with at least one more offer as they have been encouraged by news that Fox is yet to sign a contract for next season.
Walsall have opened talks with the Cheshire-based youngster, but so far the two parties have been unable to reach an agreement.
Fox could not leave for free as he is aged under 23, but any transfer fee in the summer would be set by tribunal.