O’Neill was hoping to set up an exchange using Marlon Harewood as a makeweight in the deal, but Boro have made it clear they are not interested in the striker.
Now he is weighing up an £8m bid for the England defender, who was forced to pull out of the European Under-21 Championships due to a knee injury.
Wheater has declared his intention to stay on at the Riverside despite relegation last season. And Boro boss Gareth Southgate is also keen to hang on to one of his most promising players.
But with Stewart Downing far from certain of moving until he is fully fit as he recovers from ankle surgery, Boro could yet be tempted to cash in on Wheater.