The European champions sent scouts to watch the La Liga forward during Celta Vigo's 2-0 defeat to Espanyol on Saturday. But Chelsea were not the only Premier Leauge club to watch the 25-year-old this weekend - Reading also sent representatives to run the rule over Aspas.
The Celta Vigo forward has a €10m release clause in his contract and Swansea, who have successfully scouted the Spanish market in recent months, are also thought to be interested.
Swans boss Michael Laudrup secured one of the bargains of the season when he signed Rayo Vallecano star Michu for around £2m.
And the Swans may look to return to La Liga to pick up another cut-price goal machine, although the report insists Chelsea and Reading are currently the front runners.
Aspas has eight goals for his club this season, and although he wasn't at his best as his side slumped to a 2-0 defeat this weekend, he was still his team's biggest attacking threat.
The report compares Aspas to Barcelona striker David Villa, although the 5 foot 9 inch forward has also been likened to David Silva and Juan Mata.
The Celta Vigo striker has been tipped as the next bargain from La Liga, but Chelsea may have to wait until the summer to land him, according to the report, as Aspas is keen to stay at Celta until the end of the season as they look to avoid relegation.