The 19-year-old midfielder has one year remaining on his contract and is keen to leave PSG in order to secure more regular playing time.
His asking price is thought to have been reduced down to £9.5 million from an initial price of £24 million, due to his desire to leave.
PSG manager Laurent Blanc has accepted the likelihood of Rabiot leaving, and the two London sides seem to be the front runners.
“I believe he will leave, but I can’t tell you where.”
The Parisians were keen to tie Rabiot down to a long-term deal, but competition in the squad has convinced him that his future may lay elsewhere.
Blanc said: “Rabiot has received a good [contract] offer from PSG but apparently it doesn’t interest him. It’s a shame.”
Both Arsenal and Chelsea have been consistently linked with the youngster throughout the summer, with both sides believed to still be looking to add to their midfields.