The Black Cats finished the last campaign in 10th place despite having to contend with a seemingly never-ending injury crisis, and are determined to set their sights even higher when they resume next month.
To that end, they have already made nine signings this summer and one of them, Sweden midfielder Larsson, is adamant they should be aiming as high as possible, even if Manchester United, Chelsea, Manchester City, Arsenal, Tottenham and Liverpool provide a formidable barrier.
Asked about how tough it will be to muscle their way into that exclusive club, the 26-year-old said: "Without a doubt.
"Especially with the squads they have and the money they spend, it is very, very tough. But at the same time, this is a massive club.
"I am not saying we are going to play Champions League football next season, but you have got to always keep trying to move in the right direction step by step, and hopefully that's what the club is doing right now."
Larsson, like former Birmingham team-mate Craig Gardner, headed for the Stadium of Light having endured a season of remarkable highs and lows at St Andrew's.
Both men were in the side which lifted the Carling Cup at Wembley in February, but also played in the final-day defeat at Tottenham which sent the club into the npower Championship.
However, having tasted success, albeit fleeting, Larsson is keen to sample it again with his new club.
He said: "Winning silverware and winning a title is what you dream of as a kid and it was a great day to be able to do that last season.
"Hopefully we can win something here. It's difficult, but you never know."
Manager Steve Bruce's shopping spree to date has featured Bosman free transfer captures Larsson, Keiren Westwood and David Vaughan, as well as Gardner and highly-rated teenage striker Connor Wickham, who could yet cost Sunderland £12million.
However, it is the arrivals of former Manchester United duo John O'Shea and Wes Brown which Larsson believes has sent out the most significant message to the club's rivals.
He said: "It's been really good to see the names drop in and join the club.
"I was one of the first to sign, and it's been nice to see that the club has been able to attract players like O'Shea and Brown.
"They are big players who have been at a big club for a long time, so that's a sign that the club is trying to move in the right direction.
"A lot teams talk about trying to push on and making the team better, but so far, the club has shown they mean what they are saying.
"That doesn't necessarily mean that success is going to come by itself on the pitch, but it gives us a good platform to try to move on."
Larsson arrived at Birmingham during Bruce's time at the helm, and he is looking forward to working again with a manger who has shown faith in him for a second time.
He said with a smile: "He must have liked something he saw in me the last time we worked together.
"It's good. He did show a lot of interest in me and wanted me to come here, which was a major part in my decision."