After last week's dismissal of Ruben Amorim, Carrick was named United caretaker manager to the end of this season.
Asked if he has spoken to anyone about the permanent post, the Geordie said: "No, not at the moment.
"I think we're realistic as well, and where we are at the moment, why I'm here and the role I've got to do.
"That doesn't change how we go about it day-to-day, and the focus and making decisions for the long-term strategy of the group.
"I'm certainly not coming in thinking it's a time where week-to-week, game-to-game, we've got to get through it and tick each one off.
"I think we want to plan to improve beyond this season and however that looks at this moment.
"All I can control is what we give the players and how we create the atmosphere around the group. That's the main focus, and we'll see what happens after that."
Asked if he's open to the job long-term, Carrick added: "Listen, I'm here because I enjoy the role and I wanted to do it, and I'm hugely privileged to be in this position.
"That's where I am, it doesn't change whatever the term or the length. I'm here to do my best and hopefully I've got a lot of experience of what it takes and where we need to get to, and I'll try and help with that."