The 19-year-old is being tipped as the next big thing to come out of Brazil and he has been likened to Barcelona star Neymar.
Clubs from Europe have been scouting the striker for 18 months and he already has five goals in 10 league appearances this season.
After selling Alvaro Morata back to Real Madrid, Juventus have been trying to bring in Barbosa as a replacement.
But, according to Brazilian newspaper Globo Esporte, the Italian champions are now trailing in the wake of Chelsea.
The Blues are ready to part with £25m for Barbosa, which dwarfs Juventus’ opening offer of £15m and puts them in pole position.
Santos are now ready for talks with Chelsea and a conclusion to the transfer saga is expected to be reached by the end of July.