Mundo Deportivo says Chelsea would have made an approach for Umtiti already had they not been under the transfer ban imposed by UEFA.
They add that Umtiti would have been open to a switch to Stamford Bridge and was prepared for his representative to discuss a deal with Chelsea chiefs.
In turn, Chelsea are believed to have been in touch with Umtiti's agent Arturo Canales to sound him out over a move.
The 26-year-old would prefer to remain at Barcelona, but is open to moving to a club playing Champions League football, and has a preference for Chelsea over Arsenal and Manchester United, who have also been offered his services.
Barcelona are willing to sell the centre-back at the end of the season providing their asking price of £46million is met.