The versatile wide-man, who is capable of playing at both left-back and on the left wing, arrived at Lyon from Ligue 1 rivals Lille in 2009 and is widely considered one of the best players in French football.
Chelsea, Barcelona, Juventus and Liverpool are said to be among the clubs interested in signing the Brazilian international, while Manchester United and Tottenham Hotspur were both linked with the 27-year-old during the January transfer window.
And his agent hasd revealed that two clubs have already been in direct contact.
"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," Emmanuel De Kerchove is reported to have said by Sky Sports.
"But these have been preliminary talks, nothing concrete.
"I repeat, by the end of next week we should know more."
Bastos arrived in France in the summer of 2006, joining Lille from Brazilian side Atlético Paranaense. His form in 2008/09 saw him nominated for Ligue 1's Player of the Year award, and encouraged Lyon to seal a €18 million deal for the player in July 2009.
Although he was a member of Brazil's squad for the 2010 World Cup and has been capped 11 times by his country, Bastos is not in the 23-man squad for this summer's Copa America, currently taking place in Argentina.
