According to Record, the Porto-based club have taken ‘significant steps’ to signing Garcia and Alves.
Former Benfica and Manchester City midfielder Garcia, 33, currently plays for Real Betis but does not seem to be part of Manuel Pellegrini’s plans.
And 38-year-old centre-back Alves is under contract at Serie A club Parma until June 2021.
Alves was a key figure for FC Porto from 2002 until 2010 when he moved to Zenit for €22m.
Boavista are attempting to build a squad with the ability to compete near the top of Liga NOS.
The arrival of Garcia and Alves, proven names in Portugal, could help them close the gap to leading clubs.