The Premier League duo sent scouts to watch the 25-year-old against Espanyol, a game which the Galicians lost 1-0.
Despite the result, Aspas impressed, creating opportunities for both himself and his team-mates.
His solid display may tempt both Chelsea and Reading, who are keen to mirror Swansea’s cut-price move for Michu during the summer.
Although he is not quite in the same mould as the former Ray Vallecano man, there are some similarities. However, he has been compared more closely to Barcelona star David Villa by the Spanish media due to his attacking instincts.
Aspas has spent his entire career with Celta and recently declared his willingness to stay until the end of the season to help the club fight against relegation.
But, with a reported €10m buyout clause in his contract this will not deter potential suitors from making January approaches.
His club may be tempted to cash in should they receive a sizable bid, which may persuade the forward to move on.
Having hit eight goals in 19 La Liga appearances this term, the striker is not short of admirers.
Although Chelsea would appear to be the more attractive destination for Aspas, it is unclear as to whether he would be willing to move to Stamford Bridge due to the competition for places.
This could give Reading the advantage, with the Royals likely to be able to offer him a greater chance of first-team football.