Michael Laudrup has made several shrewd signings since taking charge at the Liberty Stadium and has been linked with a winter swoop for 25-year-old forward Aspas.
Celta coach Paco Herrera stated in December that the club had no intention of letting such a key player leave, and Aspas says he will stay at least until the end of the season.
"I have read many things saying I was going to go in the winter, but they are not true," he explained.
"Already it has been said several times that at least I will be here until June 30, then we'll see what's best for the club and for me."
Aspas, who scored twice in a 3-1 victory over Real Valladolid on Sunday, has come through the ranks at Celta and still has four-and-a-half years remaining on his current deal.
"I have been at Celta 17 years and I am very proud to belong to this club," he said.
"Now I'm very calm because I have a contract until 2017."