Ferguson, who has already signed Portuguese whizzkid Nani and Brazilian starlet Anderson this summer, is keeping tabs on the 18-year-old Mexican.
Barcelona are anxious to tie Giovani down to a long-term contract which would increase his £20m buy-out clause.
Giovani has recently switched agents to Portuguese Jorge Mendes who also looks after Jose Mourinho and has done several deals for Manchester United. Barca's sporting director, Txiki Beguristain, said: "It is normal for a player of his talent to receive interest from other clubs.
"But I am calm and we are confident that he will stay and sign a new contract with Barcelona."