Larsson, who has three years of his contract to run, has been linked with a move to the English Premiership, but he insists he is going nowhere.
The Swede has assured the club's supporters he will see out the remainder of his contract at Parkhead.
Celtic's search for a central defender continues, with Norwegian, Bjorn Otto Bragstad, the latest name to be linked with a move to the club.
O'Neill has also expressed an interest in Aston Villa midfielder, Alan Thompson, though no contact has been made with the player.
Larsson, who has three years of his contract to run, has been linked with a move to the English Premiership, but he insists he is going nowhere.
"There are always a lot of rumours and speculation at this time of the year, but they shouldn't be taken too seriously," Larsson told the Celtic View.
"I've always said I'm happy at Celtic and my family are very happy too. I've no reason to go anywhere else.
"I've fully recovered from my leg break and feel strong. As a club we want a good pre-season and then we can take it from there.
"One thing's clear we have to do better than last season."
Larsson featured in Wednesday night's friendly with FC Copenhagen as a second-half substitute and provided the pass which allowed Mark Burchill to score the first of his two goals.
Celtic's defence looked shaky against Copenhagen, but following a failed £3.2m bid for Belgian defender, Joos Valgaeren, O'Neill has turned his attention to Bragstad.
The £2m-rated Norwegian is also being tracked by Derby and St Etienne, but Celtic have not bid for the player.
Out-of-favour Villa midfielder, Thompson, is another who has aroused O'Neill's interest.
He said: "His name has been spoken about but I have not spoken to him.
"I know him from Bolton and Villa and things are not working out for him at Villa.
"I won't be speaking to him tomorrow (Thursday) but that doesn't mean I won't be signing him."
Thompson has admitted he is flattered by Celtic's interest in him.
"Celtic are a great side," he told the Aston Villa website.
"They get sell-out crowds every week and it is flattering to be associated with that kind of club. But, more than that, Martin O'Neill seems to be a fantastic boss.
"I know players at Leicester who talk very highly of him and it is clear from the purchase of Chris Sutton that he is ambitious and wants to pip Rangers to a few titles."