The 25-year-old has been linked with a number of sides, including Barclays Premier League outfits Liverpool and Swansea, after notching 23 goals in Celta's promotion-winning season last term and adding a further 11 in the top flight this campaign.
However, Aspas is refusing to discuss where he might by plying his trade next season until the current one has finished.
"I've already said that I will talk when the season is over, now is not the right time to talk about this. You've talked about Valencia, Swansea and then Liverpool, that if it's one or another, but I've always said that at the end of the season we'll talk about it," he said.
"I made it very clear in December, when many thought I was going, that I wanted to help Celta stay in La Liga and then we'll see what happens, what will be will be."
Aspas and his team-mates have their work cut out to keep Celta in La Liga, though.
The Galician outfit currently prop up the standings with 31 points, four adrift of local rivals Deportivo La Coruna who occupy the last position of safety.
With Depor also having the better head-to-head record between the sides this season, Celta will essentially need to win both of their final two matches - away to Real Valladolid tomorrow and then at home to Espanyol - to stand any chance of staying up, although Aspas is not giving the fight up for lost.
He said in La Voz de Galicia: "I think that if we win (against Valladolid) we have our chances. I think that with 37 points we can get there because the other teams also have difficult games.
"By winning this weekend and going into the last weekend with options open, I think we can make the others nervous."
Valladolid are already assured of Primera Division football next season, lying nine points above the drop zone.
The future of their coach Miroslav Djukic is also up in the air but, like Aspas, he will only discuss his next step after the final game.
He said: "I'll say what I'll do after the last game in Mallorca, I haven't made a decision."
Djukic also insisted his side would be giving their all over the final two games, despite the fact they have little left to play for.
"I've always defended honesty and fair play, therefore we are going to go out on to the pitch to do what a good professional has to," he said.
"We've given our all throughout the season and we want to finish with good feelings. We're not thinking about relegating anybody, only on doing our jobs well."