The Scottish international striker is undergoing a medical at Bramall Lane and, barring any late unforseen hiccups, will be unveiled as United’s new record signing before the weekend.
McBurnie is expected to cost United around £17m upfront and will become the fourth player this summer to break United’s transfer record, after Luke Freeman, Callum Robinson and Lys Mousset.
And, in his press conference ahead of their opening game against Hull this weekend, Cooper told WalesOnline: “We just need to look forward.
“It’s a deal that’s been done by the club and first of all we have to wish him [McBurnie] well. He’s a fantastic person and a really good player.
“We’re all very proud of him. If we stand still, we lose ambition and motivation. I really believe in what we’re doing here and that hasn’t changed with the news of the last few days.”
McBurnie scored 24 goals in all competitions for the Swans last season, and follows Daniel James out of the exit door after he joined the Blades’ Premier League rivals Manchester United.
“The club wishes them both well,” Cooper added.
“Oli’s not quite done. But it’s not abnormal to lose good players. You look at Norwich this time last season and what they went on to do.
“I’m not saying we’ll do that but it’s not an unusual situation. We really believe in the players that are in the building and they’re proud to play for the football club. We believe that any game we play we’ll be more than competitive if we get it right.”