Lancenet claims the Stamford Bridge club have already made an offer for the highly-rated defender, believed to be €9.4m.
But third parties own 60 per cent of Doria's economic rights, which means Botafogo would only receive €4m for the player.
The report claims the bid was lodged through Carlos Meinberg Neto - the same agent who represents Chelsea star Oscar - and Botafogo are expected to respond before the weekend.
Chelsea's squad already has several Brazilian players, including Oscar, David Luiz, Ramires, Lucas Piazon and their most recent addition Wallace.
But they face stiff competition from a number of top European clubs for the signature of the 18-year-old.
Juventus, Barcelona, Tottenham, Porto and Benfica have all been linked with the defender, as scouts have flocked to watch the youngster in action.
And a separate report carried by talkSPORT claims the intense interest in the teenager could spark a bidding war for his services.
He first broke into the Botafogo first-team in 2012, before making his Brazil debut earlier this year.
He also helped the Brazil under-20 team to the Toulon Tournament title this summer.