The Italian looks set to leave Stamford Bridge this summer after just two years in charge.
Conte has been linked with a number of jobs for next season, including Inter Milan and Paris Saint-Germain.
But, according to Don Balon, the Italian is now a shock contender to take charge at Barcelona.
The Spanish club flopped in the Champions League this season and manager Ernesto Valverde is under pressure.
And, should the 54-year-old be shown the door, then Conte is in contention to take charge at Barcelona next season.