The 20-year-old Frenchman joined the club from Rennes for £23m last summer, signing a seven-year deal with the option of an extra 12 months.
He featured regularly in former manager Mauricio Pochettino's sides in the first half of the season, before a hamstring injury ruled him out from December until May.
Ugochukwu is rated very highly at Stamford Bridge but given their large squad, it's expected that first-team opportunities will be limited this season.
A move to Southampton could give him the regular first-team football needed to help boost his development, while also allowing the Blues to trim their squad for the upcoming campaign.
Lesley Ugochukwu (right) is currently in talks with Southampton over a potential loan move
Mail Sport previously reported that Chelsea will look to raise over £200million in player salesas they enter the final phase of another extraordinary window that has seen rivals question how they can continue to spend so lavishly without reprisals.
The £54million signing of Pedro Neto from Wolves this weekend was their 12th of the summer but won't be their last.
Atletico Madrid striker Samu Omorodion should have been next through the Stamford Bridge revolving door only for negotiations to collapse on Sunday evening.
Attention has switched to Joao Felix - who previously spent a year on loan at Chelsea - and the club also want another centre forward, with Napoli's Victor Osimhen heavily linked.
Potential players to exit include Romelu Lukaku, who wants to join Napoli, Trevoh Chalobah, an option for Crystal Palace, and Armando Broja, who is on Stuttgart's wishlist and admired by Wolves.
Conor Gallagher appeared to be on the verge of a £35m move to Atletico Madrid, though that deal has stalled since Omorodion's move in the opposite direction fell through.
Southampton would have to complete the signing of Ugochukwu before midday on Friday to include him in their matchday squad for the opening Premier League fixture at Newcastle on Saturday.