The Blues initially wanted €7 million according to the report but the Lions are reported to have negotiated the price down to €7 million.
The 21-year-old who spent last season on loan with Dutch side Vitesse is being targeted to strengthen the right side of midfield and can also play as a fullback.
The Brazil under-20 international, signed from Fluminense in 2013 and was one of three Blues players who spent last season on loan at Vitessse.
Galatasaray won the Süper Lig title for a record 20th time last season earning the right to wear the fourth star on their shirts.
The Istanbul giants booked a place in the Champions League group stages for the fourth consecutive season.
The Lions recently completed the transfer of Arsenal striker Lukas Podolski on a three-year deal and are expected to make more signings over the transfer window.