Manchester United, Chelsea, Arsenal and Liverpool are all keeping close tabs on the skilful attacking midfielder - touted as a successor to Ronaldinho at the Nou Camp - who will make his debut for Mexico against Panama today.
The Daily Mail says Pini Zahavi, who fixed Roman Abramovich's deal to buy Chelsea and who has negotiated many transfers for United, will act for Giovani in November.
Zahavi said: "Until then I will not speak to anyone about him. There has been no contact with English clubs. But obviously Giovani is a diamond of world football. He has a contract until 2008 but he signed when he was under 18, so you can look at that how you wish."
Barca fear that Zahavi's links with Roman Abramovich and Sir Alex Ferguson mean they may have to break their budget to keep him.
Dos Santos, son of former Brazilian player Zizinho, has a European Union passport and will not require a work permit.