Tynecastle officials enquired about the 21-year-old and City are receptive to a season-long loan deal. Negotiations are taking place at the moment for the proposed move to Scotland.
Smith-Brown is an attacking left-back who has represented England at every youth level up to under-20. He spent last season on loan in the Netherlands with NAC Breda, playing 29 games and helping the club secure promotion to the Dutch top flight.
He joined City’s youth academy aged five and progressed through their system to captain their under-18 side. Coaches there feel he needs more first-team experience and want him to go out on loan again next season.
Hearts believe he could solve their problem left-back position after trying three different players there in the last two years. Juwon Oshaniwa, Faycal Rherras and Lennard Sowah have all failed to cement themselves in the side, and the latter two were released last month.
Head coach Ian Cathro intends to use a three-man defensive system with two wing-backs next season, and Smith-Brown has been earmarked for a role wide on the left.
The player is interested in moving to Edinburgh and both Hearts and Manchester City appear keen to complete the loan agreement.