Mundo Deportivo says the Nou Camp giants would be willing to enter talks with Everton over a move to get Umtiti's wages of the books. The Spanish publication adds Barcelona could cut their 12m euro (£10.7m) asking price to get a deal over the line.
The 27-year-old is mooted to earn around £75,000-a-week at Barcelona.
Umtiti has struggled in recent seasons to maintain his fitness on a regular basis due to persistent knee issues but for manager Carlo Ancelotti, he could be an intriguing gamble for his Goodison Park rebuild.
He has played 31 times for France and was a part of their World Cup winning squad in 2018, starting the final against Croatia which his side won 4-2.
Umtiti joined Barcelona in July 2016 in a £21m move from Lyon and for the first two years in Spain, was an ever-present in the side.