The 19-year-old became a free agent at the start of July, having elected not to extend his terms at the London Stadium after 18 senior appearances for the Hammers in all competitions.
Mubama's future was the subject of uncertainty for several weeks, but earlier this month, City emerged as shock contenders to snap up the 2004-born attacker.
Pep Guardiola's attacking ranks have been thinned by Julian Alvarez's blockbuster move to Atletico Madrid, as well as Oscar Bobb's leg fracture, which will sideline him for several months.
According to Football Insider, Mubama arrived at Man City to undertake his medical examinations on Wednesday, and there is optimism that a deal will be concluded within the next 24 hours.
Man City 'to pay £1.5m compensation' for Mubama
Even though Mubama became a free agent at the end of the season, he will not arrive at the Etihad for nothing, as the report adds that Man City will fork out a £1.5m compensation fee to West Ham.
The Premier League champions are said to have hijacked Mubama's proposed switch to Portuguese Primeira Liga side Famalicao, but he will likely join up with the club's youth academy first.
Nevertheless, the Etihad powers-that-be apparently believe that the 19-year-old can blossom into a fundamental player for City in years to come, having enjoyed prolific seasons at youth level while knocking on the first-team door at West Ham.
Mubama only made a fleeting impression under David Moyes, scoring just one goal and setting up another in his 18 appearances, both of which came in West Ham's triumphant 2022-23 Europa Conference League campaign.
The 6ft striker - who has four caps for the England Under-20 side - made five appearances for the Irons in the 2023-24 Premier League season, but all of those matches came from the bench.
Mubama to be first of three Man City signings?
Should Mubama's deal indeed go through on Thursday, the 19-year-old could potentially be the first of three new signings for Guardiola's side in the coming days, although one of those potential arrivals is already well-known to the Citizens faithful.
Just one year after leaving the Etihad for Barcelona, Ilkay Gundogan is now said to be on the verge of a return to Manchester on a one-year deal, and Man City will not pay their Spanish counterparts a penny for the German midfielder.
Furthermore, with Alvarez gone, Bobb sidelined and Mubama expected to start out in the academy, Man City have apparently cast their eye over to Scotland, and in particular Celtic's Kyogo Furuhashi.
The 29-year-old has scored 73 goals in 135 matches for the Bhoys over the past three years and was briefly linked with a move to Tottenham Hotspur when Ange Postecoglou swapped Celtic for North London.
Spurs signing Dominic Solanke has closed off that avenue, but Celtic remain under no pressure to sell Furuhashi, who is under contract with the Scottish champions for another three years.