The Turkish sports newspaper report that PSG have been keeping close tabs on Telles over the past season.
Telles was part of the Galatasaray side that won the league title for a record 20th time last season. The Lions also won the double and earned the right to wear a fourth star on their shirt next season.
The French giants could however, face competition from Premier League champions Chelsea.
Sky Italia reporter Gianluca Di Marzio reports that the Blues are favourites to sign the 22-year-old Brazilian.
Telles joined Galatasaray on a €6 million transfer from Gremio last January and still has another three-years left on his current deal.
The young Brazilian provided a total of two goals and three assists in 56 games for the Lions last season.
Galatasaray have booked a place in the Champions League group stages for the fourth season running.