The highly-rated forward will cost any potential suitors €10million (£8.3m), with Celta in no mood to compromise on a deal.
They will, however, have no choice but to enter into discussions if their valuation of Aspas is met.
Chelsea and Reading are among those said to be keen, with the Premier League pair in the market for new recruits.
Celta are hoping no bids will be tabled by the end of the month, but concede that mounting interest is likely to see their hand forced.
Coach Paco Herrera said: "It seems that there is the possibility of a club emerging that are willing to pay the clause.
"In that case, if the player wants to go, Celta will not be able to do anything."