The striker is being watched by Liberty Stadium boss Michael Laudrup and has also been linked with Arsenal and Atletico Madrid.
Aspas has scored six goals this season and his agent has indicated a move could happen any time after the winter transfer window opens on Tuesday.
But Herrera has been given assurances about keeping the 25-year-old by Celta president Carlos Mourino, although the situation may be less certain in the summer.
Herrera told Spanish media: "The president has made it clear Iago will not leave until the end of the season, so I am quiet."
But Herrera fears Aspas' head may have been turned by the speculation about his future in the media.
"What worries me is he could be lost in other things," said Herrera.