The 19-year-old Brazil international is understood to be a target for several European clubs after emerging as one of the most exciting young talents in South American football.
Talk of an offer from Inter Milan was recently played down, while the player has insisted he is remaining calm over his future.
Fresh reports have suggested that Manchester United have tabled a bid in the region of £26million, but Sao Paulo have no intention of cashing in on the youngster.
“It is a risk not selling Lucas, but we are going to take it,” president Juvenal Juvencio is quoted as saying in the Daily Mail.
Manchester United manager Sir Alex Ferguson stated on Thursday that he was looking to bring in at least one more player this summer, while Chelsea and Real Madrid have also been linked with a move for Lucas.