United have expressed interest in signing Tottenham striker Kane and Chelsea midfielder Mount as well as West Ham captain Declan Rice and Paris Saint-Germain superstar Neymar.
Manchester United have enjoyed a promising first season under Erik ten Hag, winning the League Cup, reaching the FA Cup final and all but securing a top-four finish.
‘I’m sure we’re going to make new signings, big signings this summer, so hopefully we can get them done as quick as possible so they’re in for pre-season,’ Shaw told sky sports.
‘Our aim for next season has to be winning the Premier League and the Champions League.’
Shaw is confident Manchester United are ‘coming back’ under Ten Hag, having won their first trophy since 2017 under the ex-Ajax boss.
The Red Devils, once the dominant force in English football, have largely struggled since Sir Alex Ferguson’s retirement a decade ago.
‘I think teams around us can definitely see that United are coming back,’ the England left-back added. ‘First season under the new manager, I think there’s always going to be a bit of transition.
‘But it’s clear to see what he’s brought in and how he’s changed the way we think, the way we play.
‘I think he wants to bring in a lot of intensity – everything he wants the team to do is high intensity.
‘He wants us to be aggressive on the front foot, pressing as high as possible, but also with the ball. I think he’s made us better, we’re definitely more of a threat now with the ball and when we’re on the ball.
‘It’s clear to see we’re going in the right direction and like I touched on before, we have to be challenging for the title.’
Manchester United face Chelsea in their penultimate game of the season on Thursday night, knowing a point would secure a return to the Champions League.
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