No firm offers have been tabled for Shittu yet and Hornets chairman Graham Simpson has denied that bids would be welcomed.
"We have had inquiries from Premier League clubs but no offers for Danny," Simpson told BBC Sport. "Danny is still with us and that's the way it is staying."
However coach Malky Mackay previously admitted: "He is under contract and would be a big-money signing. Whether the club wants to sell, I don't know, but every player has his price."