The Lyon midfielder has been linked with a move away from Ligue 1 for some time, with Serie A giants Juventus having led the chase.
Juve remain in contention to secure the Brazilian's signature, but they now face stiff competition from elsewhere.
Chelsea, Inter Milan, Barcelona, Liverpool and Tottenham are all believed to be monitoring Bastos' situation.
His representative admits two of those clubs have already made tentative enquiries, with the battle to land the Samba star set to hot up.
Emmanuel De Kerchove said: "All of them are big clubs and, indeed, two of them called me to find out if the player would be interested and to possibly speak to him about their project.
"But these have been preliminary talks, nothing concrete. I repeat, by the end of next week we should know more."