Mata, who joined from Premier League rivals Chelsea for £37.1 million ($61.2 million, 44.8 million euros) earlier this month, made his debut for United in the 2-0 win over Cardiff on Tuesday.
That match saw Robin van Persie and Wayne Rooney return from injury lay-offs, and both will be in contention for a place at the Britannia Stadium on Saturday.
It would mean United’s star strikers starting together for just the eighth time in 24 Premier League matches this season. The availability of the three players means other places in the front four are sure to be squeezed.
England winger Young, who will be battling with Adnan Januzaj, Antonio Valencia and Danny Welbeck for the last spot in manager David Moyes’s strongest side, said: “You have to be on the ball. You have to put in big performances every week. We have a big squad and we can rotate the team.
“When you are playing well, getting goals and assists, you are there in the manager’s thoughts,” added the 28-year-old, who scored United’s second goal against Cardiff following Dutch striker van Persie’s sixth-minute opener at Old Trafford on Tuesday.
“We have competition for places and that keeps you on your toes. You want to keep playing well and training well, because that is the only way to keep yourself in the team,” Young explained.
“Robin is a goalscorer. You put him in the box and he will score, and he has done that again.
“There will be a lot of talk about Juan’s arrival and the fact that we have broken the transfer record for him, but he looks like he has been here for years.
“It was his first game but he has gelled straight away with the way we play. He is going to add something special to the squad.”
But Saturday’s game is likely to come too soon for Marouane Fellaini, who has been absent since December with a wrist injury, while fellow United midfielder Michael Carrick is also set to miss out with an ankle problem.
Winger Nani has been sidelined with a hamstring injury since December 7 and is unlikely to return against former United striker Mark Hughes’s Stoke side.
Despite beating Cardiff, United are still 13 points behind leaders and local rivals Manchester City and six adrift of the fourth Champions League spot currently occupied by bitter foes Liverpool.
United’s latest trip to the Britannia Stadium, where they have won five and drawn one of their six previous visits, comes with Stoke just three points above the relegation zone after a midweek 1-0 loss to Sunderland.
The Potters have lost their last three matches, all by a 1-0 scoreline, and face a difficult schedule with games against United and Manchester City in the weeks ahead.
But Stoke goalkeeper Asmir Begovic said: “It’s so tight but there’s no panicking around the club.
“The manager (Hughes) is dealing really well with it. He’s praised everyone and just wants us to keep our heads up.”
Bosnia international Begovic added: “We’re not getting the luck that we deserve at the moment. As long as we stick together, though, and keep doing the right things, we believe we can progress up the table.
“We’re definitely not panicking, we’re just going to try and keep performing.”
Stoke midfielder Steven Nzonzi is suspended after his red card in the defeat at the Stadium of Light but German defender Robert Huth could return following a knee injury.