Manchester United has had two bids for Branthwaite rejected earlier in the transfer window, though the Red Devils expected to try again to draw the defender away from Goodison Park.

Everton announced the signing of O'Brien on a four-year contract after an impressive season in Ligue 1.

Among Lyon players, O'Brien made the most blocks (18) and clearances (96), while only Duje Caleta-Car (57) won more contested aerial duels than his 44.

The Republic of Ireland international is the fifth signing for Everton so far, and Dyche explained why he felt it was so important to use this transfer window to build for the future.

"Putting two and two together at Everton football club. No way!" Dyche said.

"What I would suggest is, it's nothing to do with that. It's just trying to model the club with the finances available. Trying to bring in players who can add to the layers of the club.

"Obviously, we're stretched at the moment, but the depth of the club, with a younger style of players who can develop and protect the club both on the pitch with their performances and in the future with the finances.

"It's a tough juggling act and tough to find the players who can do that, but we think we've got a few here now.

"We've made it clear to him [Branthwaite] that there was nothing other than that. But like you said, put two and two together and everyone starts speculating. What can you do?"