The 2019-20 WSL season was United's maiden year in the English top flight after they won promotion from the Championship one year after the side was formed.
Press' signing from the Utah Royals, alongside that of USWNT teammate Tobin Heath, was a massive coup for the club with United manager Casey Stoney noting that it sent a message to the rest of the league about their intentions this season.
"For me personally I will always say that I'm here to win. I think that's just the top priority," Press told ESPN.
"I think here it's just going to all be about winning titles. That's the cups, it's qualifying for Champions League, I feel like that's a title in itself especially for a young club like Manchester United.
"I think it will be tough and the strongest teams here will be a challenge and that's why I'm here. To help with that challenge and help the team compete for titles."
While Press acknowledged it would be a challenge with the top three of Arsenal, Chelsea and Manchester City well established in the league, she said she was confident the squad could achieve big things under Stoney's leadership.
"I think Casey's reputation is really strong and it is a strong reason why I thought Manchester United would be a good fit for me this season," Press added.
"Getting here and meeting her and hearing how her staff and her team speak about her, I don't think I've ever heard and seen people speak more highly of a manager so that makes me incredibly excited to learn and grow under her."
"One thing I admire is the humility that she has and that she expects all the players to have every day and I think that's such an important thing when you're trying to have a growth mind set, is to bring a work ethic and humility."
The 31-year-old does have experience of playing in Europe spending two seasons in Sweden between 2012-2014 and another three month loan stint in 2018.
"I think the experience is invaluable and I saw that the last time I was in Europe. You just learn so many different elements of the game and you learn different players and you see them in a different light." Press said.
"International football is always like a shooting star type of moment and you come into this high pressure situation and some people shine and some people don't and being in a club environment you take things a lot more slowly and you're able to learn.
"You're able to see people and their flavour and get to know them deep inside as to who they are and what makes them tick and I think that exposure to different types of people, different types of upbringings is huge for me.
"I think it is one of the things I love the most about the game is how it offers the opportunity to always learn, to always get better. There's no such thing as perfection so the more exposure you have the better off you are.