The 19-year-old has become a regular member of the Rennes first team setup under Bruno Genesio and has already represented Les Rouge et Noir on 60 occasions in all tournaments.
Ugochukwu has come up with one goal and one assist for his current club in that time, while he started 14 games in Ligue 1 and a further five in the Europa League last term.
Primarily a defensive midfielder, Ugochukwu - who stands at 6ft 3in tall - has also earned nine caps for France's Under-19s, scoring two goals in the process.
The 2004-born lynchpin is only under contract at Roazhon Park for another two years, though, and his promotion to the Rennes first team unsurprisingly attracted interest from elsewhere.
According to Sky Sports News, Chelsea have now won the race to prise Ugochukwu away from Rennes, who will receive €27m (£23.2m) for the sale of the 19-year-old.
While Chelsea's current midfield shortage is well-documented, the report adds that it is still unclear whether Ugochukwu will be thrust straight into the first team or sent out on loan for the 2023-24 campaign.
Chelsea's owners BlueCo recently acquired a majority stake in Rennes' Ligue 1 rivals Strasbourg, who could take Ugochukwu on a temporary deal in order to offer him more minutes at the top level.
The Blues are on the verge of sealing a deal for Ugochukwu after being knocked back by Brighton & Hove Albion in their pursuit of Moises Caicedo, who has supposedly been the subject of a failed £80m offer from Mauricio Pochettino's side.
The Seagulls are adamant that Caicedo will not leave the Amex for less than £100m this summer, although the Ecuadorian is reportedly ready to plead with Brighton to lower their demands.
Chelsea are not expected to encounter any problems agreeing personal terms with Caicedo, but the Blues are not reported to be in any active discussions with Brighton after their second failed approach.
Pochettino has already overseen a mass exodus of midfielders this summer, allowing Mateo Kovacic, Mason Mount, N'Golo Kante, Tiemoue Bakayoko and Ruben Loftus-Cheek to move on.
As a result, Enzo Fernandez and Conor Gallagher represent Chelsea's two most experienced midfield options at present, although Carney Chukwuemeka, Andrey Santos and Cesare Casadei have all enjoyed first-team action in pre-season.
Gallagher is still being linked with an exit from Stamford Bridge amid supposed interest from West Ham United, but Pochettino has insisted that the Englishman is in his plans for the 2023-24 season.
Chelsea's penultimate pre-season match sees them take on West London rivals Fulham in Maryland on Sunday, before Pochettino's side cap off their preparations against Borussia Dortmund in Chicago next month.