The England centre-half has been the subject of two rejected bids already as the Toffees hold out for £70million before they consider selling their prized asset. The Red Devils have gone up to £50m, but haven't returned with a fresh bid since, having initially offered £35m.
Everton have landed O'Brien from Lyon, but their manager maintains the Irishman will add to their defensive resources - not serve as a replacement for Branthwaite.
Dyche was quizzed by Sky Sports on the matter and replied as cited by Sports Central: "No way! You’re kidding me! I’m very surprised you’ve put two and two together at Everton Football Club. It’s nothing to do with that. It’s just to do with trying to model the club with the finances available. Obviously we’re stretched at the moment with depth. "Trying to bring in players who can add layers to the club. Younger players who can develop and protect the club both on and off the pitch with their performances and then in the future with the finances. It’s a tough juggling act and it’s tough to find the players who can do that. We think we have a few here. "We’ve made it clear to him [Branthwaite] that there’s nothing other than that. But of course put two and two together and everyone starts speculating. What do you do?"
Everton have already allowed one of their leading lights to leave in Belgium international Amadou Onana, who joined Aston Villa and banked the Merseysiders £50m in the process, easing financial pressures.
United's need to bolster their backline has just increased after new signing Leny Yoro suffered a pre-season injury on his debut. He's been pictured on crutches and could be sidelined for a prolonged period.
Erik ten Hag has already admitted that, despite spending more than £50m on Yoro, they would be open to signing more defenders.
He said: "I think we are occupied [in that position] but we work continually. "The good thing is we already signed two players, but it belongs to a club like Manchester United that you are still looking - if the opportunity is there for better and we still have time, until August 30."
