The 22-year-old striker joined on loan from Getafe in September, but is yet to open his account in 10 appearances for the Swans.
However, only two of those have come as a starter.
Despite that, Vazquez said he is enjoying life in South Wales, due mainly to the strong Spanish contingent at the Liberty Stadium.
"I'm very happy in Swansea," the former Spanish Under-21 international told Wales Online. "I'm living here with my family and it's a really good club to be at because of the Spanish players and the rest of the team.
"I'm really happy playing in the Premier League and I would love to stay at the club for longer.
"I'm trying my best to convince the manager. If I do well in the next few games then I hope it will help me."