Victor Lindelof is the only arrival so far, however, setting United back around £31m to sign from Benfica, though Yorke is confident that the lure of Champions League football next term will make Mourinho's task of persuading others to join a little easier.
"United are obviously looking to add to the squad, we know that, that is not a secret," he told Sky Sports News. "It's all about the quality that is brought in. I'm sure Jose's got his targets like every other manager.
"I think that Manchester United being the richest club in the world, in the Champions League as well, things are looking pretty up. I believe that come the start of the season we will get three or four quality players in and make sure we are competitive enough and raring to win the Premier League this season.
"Winning two major competitions for us last season helps us, being in the Champions League this season also helps us and puts us back in the forefront of things. As I said we're one of the richest clubs if not the richest club in the world right now so we can attract all the players.
"Mourinho's been able to do that without the Champions League, now that we are in the Champions League, I think we are in a position to strike. I do believe that this season is a year that we're going to try and win the Premier League."
United are thought to have prioritised signing a couple of attacking players before the new season, having offloaded out-of-contract striker Zlatan Ibrahimovic earlier this month.