The Barclays Premier League newcomers are lining up a shock move for the out-of-contract Villarreal midfielder, 34, and his representative Ely Coimbra says a deal could be struck.
Coimbra told the Western Mail: "Marcos Senna had a previous conversation by phone with Swansea manager Brendan Rodgers and that made him very proud and honoured with the possible interest of Swansea to have him in the squad for the Premier League."
He added: "Marcos is very happy with the possibility and of course keen to play Premier League football, but we want to make very clear that we are right now on preliminary contacts.
"But of course Swansea City can be a very attractive option, since Mr Rodgers explained to Marcos his ideas about his team and part of Swansea's project - which pleased him a lot - and obviously because of the nice and vibrant city of Swansea."
Senna won 28 caps for Spain and was part of the squad that won the European Championships in 2008.
Source: PA
Source: PA