The move follows United's £4m deal, rising to £8m with add-ons, agreed with Tottenham for winger Tynan Thompson earlier this week, subject to the completion of his registration. Manchester United are now understood to be close to finalising both City deals, with the club hopeful of getting the pair of 16-year-olds over the line.
Eze, who has captained England's Under-16s, is also eligible to represent the Republic of Ireland having been born in Dublin before his family moved to Manchester when he was six. A powerful box-to-box midfielder, he has already featured for Manchester City's Under-17s side.
Cassim, meanwhile, was part of the City Under-18s side that beat United in last season's FA Youth Cup final, and has represented England Under-17s alongside United's own rising midfield talent, JJ Gabriel.
Should the moves for Eze and Cassim be completed, both players would join United's age-group teams at Carrington rather than being fast-tracked into senior involvement, in contrast to Thompson, who is being integrated straight into the first-team set-up as part of the club's emerging talent pathway.
The trio would represent the latest in a string of academy-level additions for United this summer, as the club continues to invest heavily in recruiting young talent from rival Premier League academies.
Poaching prospects from City would extend a pattern United have followed in recent years under their INEOS-led sporting structure, having previously brought in highly rated youngsters Ayden Heaven and Chido Obi from Arsenal's academy.
Both Eze and Cassim are considered among the most promising talents at their respective age groups within City's system, and their departures, should they be finalised, would represent a notable loss for a club that has invested heavily in developing its own academy pipeline in recent seasons, reports the Daily Mail.
The moves also underline United's continued focus on strengthening across every level of the club this summer, from first-team recruitment down to academy prospects, as the Old Trafford hierarchy looks to build a deeper pool of talent to support Carrick's plans over the coming seasons.