City have reportedly put £50million aside to invest in young British talent, and that puts both Barkley and Shaw high on their list of priorities.
There is concern at the Etihad surrounding the number of home-grown players likely to start at the club next season, which must include eight of the 25-man squad.
And City could face the prospect of losing some they already have, with Micah Richards and Jack Rodwell both linked with summer moves away.
Joleon Lescott could be another one to depart, while Gareth Barry is unlikely to return from loan at Everton.
City did not have one British player in their starting line up in the Capital One Cup final last Sunday.
They have been watching Everton starlet Barkley for some time, while 18-year-old Luke Shaw – who made his England debut last week – is the most wanted young player in the country, with Chelsea and Manchester United both chasing his signature.