The 25-year-old has attracted attention from a number of clubs - not just in the Premier League - after an impressive record of 25 goals in 37 matches last season, to help the Spanish club to promotion.
Aspas has made a seamless transition stepping up to the Primera Division in 2012/13, and is now rumoured to be on the radar of Blues interim boss Rafa Benitez, who is considering a bid to bring his compatriot to Stamford Bridge this month.
Chelsea have already signed Demba Ba in a £7million deal from Newcastle United, but could still move for the talented Spaniard as the European champions look to bolster their ranks even further.
Valued at around £10million, Aspas will not come cheap, but after Roman Abramovich bankrolled the £50million club-record signing of Fernando Torres, the deal would be relatively inexpensive by comparison.
However, Reading will not be challenging Chelsea for the player's signature, after McDermott explained: "I would be surprised if anyone could do that deal. It's an expensive deal and a difficult one for anyone to do.
"I've seen him play, our scouts have seen him play and he has had a couple of really good seasons. We know him - but it's a very difficult deal to do.
"Celta Vigo are a big club. The money that they are talking about on this player (Aspas) is a fortune."