Fulham are desperate to keep Davis having already rejected two bids by Everton for the player.
"I need players to improve my squad because we haven't really replaced what we lost last season and Sean Davis is certainly a player I admire," the Boro boss told BBC Online.
"Sean is a player I have always admired and obviously there is speculation about him wanting to leave Fulham.
"But, at the present moment there is nothing going on to indicate that he is coming to Middlesbrough.
"I think Fulham don't really want to sell him and I can understand that."