Director of football Frank Arnesen has been monitoring the 18-year-old's progress for some time.
Sturridge's current deal runs until the end of next season, but City boss Sven Goran Eriksson is keen to tie him down on a longer contract, says the People.
Sturridge, the nephew of former Derby striker Dean and Stoke star Simon, has been wrapped in cotton wool by City bosses including Kevin Keegan and Stuart Pearce, but it appears the Swede is now ready to give him his chance.
Eriksson has spoken of looking after Sturridge and making sure his development isn't rushed. But he now faces the dilemma of nurturing the talent or using a player he knows will get goals.
Chelsea would love to acquire Sturridge at such an age but City will do all they can to keep him.
Sturridge, who signed a deal with sportswear giant adidas when he was just 13, is an Arsenal fan and Gunners boss Arsene Wenger is another manager who is keeping tabs on his progress, as is Manchester United chief Sir Alex Ferguson.