The Sunday Mirror reports that Bruce will step up his interest in the duo this week.
Birmingham winger Larsson is available on a Bosman, while Campbell has a £1million buy-out clause in his contract.
The Black Cats face competition from a host of Premier League clubs for the duo.
What is your opinion? Feel free to discuss the article under. You have to comment by using your Facebook profile. Be fair and have respect for other people and opinions!
Liverpool have unveiled their new home kit for next season, sticking with the hugely popular retro styling of the current shirt.
The reputation of the Premier League means it is the most popular and one of the most watched leagues in the world.