It has been reported that Everton have identified the 24-year-old left-back as a long-term successor to Leighton Baines.
Baines, 33, has been on the books of the Toffees since the summer of 2007 when he joined from Wigan Athletic for an initial transfer fee reported by BBC Sport to be worth £5 million and earns £70,000 per week as salary at the Merseyside club, according to The Daily Star.
Everton, though, could face competition for the services of Bryan in the summer transfer window.
According to a report in The Sun earlier this month, Championship club Aston Villa are interested in securing the services of the 24-year-old left-back.
Underwhelming for Everton fans?
Bryan is a very good left-back who has proved himself in the Championship and could well be playing in the Premier League with City next season.
However, the 24-year-old could be seen as an underwhelming and unfashionable signing by the Everton fans.
After all, Bryan is not exactly a big name in the world of football and has no experience of playing in the Premier League.
Signing the 24-year-old left-back would be a risk for Everton, but he could well develop learning from Baines, who still has a fair few years left in him.