Portuguese newspaper Jornal De Noticias claim Mario's agent Kia Joorabchian delivered the offer along with a matching bid from Inter Milan which also included £4m in bonuses.
The report says Sporting are leaning towards accepting the Blues' bid because the Premier League club will reportedly pay more of the money upfront.
Mario is also said to favour a move to the Premier League but Noticias claim he is currently fully focused on Sporting.
The Portugal international, however, is not against a move away from the Estadio Jose Alvalade and is merely awaiting for the clubs to agree terms.