Hodgson is keen to bring in Silva as a replacement for Javier Mascherano who looks set to make a £25million move to Barcelona, according to the Daily Mail.
Silva will be allowed to leave Panathinaikos this summer, due to the financial crisis in Greece.
Hodgson is also reportedly considering making moves for Fulham duo Brede Hangeland and Danny Murphy and Real Madrid star Rafael van der Vaart.