The Dutch forward was seen as a somewhat uninspiring January arrival but has won fans over with several impressive performances, none more so than in the Swans' win at Sunderland on the final day.
And with Swansea reportedly keen bringing Emnes back again next season, the 25-year-old is hoping both parties can agree a fee.
"It's always nice to play in the Premier League, and that has always been my ambition," Emnes told the South Wales Evening Post.
"I had a good time with Middlesbrough, and I'm having a really good time with Swansea at the moment.
"I would like to stay in the Premier League, so wherever that is going to take me, I hope that is what happens."