The 31-year-old striker, who was a part of his country's 2010 World Cup and Euro 2012-winning squads, joined the Swans from Sevilla.
He now hopes to emulate former Swan Michu in playing for Spain while plying his club trade at the Liberty Stadium.
"I would like to return to play for Spain, it would be a very special thing for me," said Llorente.
"I would like to get back into the national side and I know that I will need to play well for Swansea all season if I want to do that."
Llorente won the most recent of his 24 caps in 2013, though there is a precedent for Swansea players representing Spain.
Former forward Michu was rewarded for a prolific first season for the Swans - in which he scored 22 goals - with a debut for the then world champions against Belarus in 2013.
Llorente would like to emulate his countryman's goalscoring exploits, as well as Michu's feat of winning silverware in his first season with Swansea in the form of the 2013 League Cup.
"I would like to score a lot of goals like him. He has done very well here and I need to work hard if I am to perform like him," said Llorente.
"I think it is possible to win one of the cups. We know winning the Premier League is a very difficult competition with a lot of teams at a high level but we want to do well."
After successful spells with Athletic Bilbao and Juventus, Llorente scored only seven goals for Sevilla in all competitions last season as he struggled to secure a regular starting role.
He is likely to face similarly stiff competition for places at the Liberty Stadium, with Swansea set to complete a club-record £15m signing of Atletico Madrid striker Borja Baston.
"He [Borja] is a good player, he will be important for Swansea. I need help from all the players and I need competition," said Llorente.
"My year in Sevilla was not very good for me but now I want to change this situation and score more goals for Swansea and show my best performance like I showed with Athletic Bilbao and Juventus."
Fernando Llorente hopes to force his way back into Spain's squad by impressing for new club Swansea City.