The Reds kickoff their group phase against LASK Linz on Thursday.
Mac Allister told TNT Sports: “As every big team, you want to aim very high.
“We've got an important competition like the Europa League and then the Premier League of course. We want to get this club back into the Champions League.
“So we have to aim very high and that's what we are trying, try to go step by step, win every game and then the future we will see. But of course, at this big club, we will fight for everything.
“We all know how important the Premier League is, it's a whole year, and when it's that long, the best team gets the trophy.
“We are still improving and we are really happy with our performances so far. That's 100 per cent our aim."