Bastos had been strongly linked with a move to Serie A rivals Napoli, but the capital club now appear favourites to sign the 30-year-old.
Roma have already added Radja Nainggolan to their ranks after agreeing a deal to sign the midfielder on loan from Cagliari, with a view to a permanent deal.
Garcia previously managed Bastos at Lille and admitted he had been keen to work with the forward ever since he left for Lyon in 2009.
"It’s not done yet (the deal), but negotiations are at an advanced stage," Garcia said after Roma's 3-0 win over Livorno.
"He is a versatile player, which is what interests me. He can play on the right or left, has a strong shot, good technique and can also play left-back, so we are covered in many different areas.
"I have been tracking this player since he left Lille, going through Lyon, Schalke and Al Ain.
"I always spoke to him and knew this was a possibility for us.
"Above all, he was very eager to come back to Europe, so I am happy. He’s not just a player of a top level, but also a good man."
