Serran, 25, suffered an injury-hit season in his second year at the Liberty Stadium.
He has been limited to just 25 appearances since joining for £80,000 from Spanish side Espanyol in 2008.
Swansea have also offered new deals to Leon Britton, Fede Bessone, Andrea Orlandi, Shaun MacDonald and Jamie Grimes.
Source: BBC Sport
Source: BBC Sport