Valencia have already been in talks to bring in the full-back but Del Horno's former club could become a major rival in the bidding war.
"We are ready to equal the €7 million ($8.7 million) offer made by Valencia to Chelsea for Asier Del Horno," Bilbao president Fernando Lamikiz was quoted as saying by Sky Sports Network.
"Then we would have to analyze the player's salary and negotiate with him," Lamikiz said.
The Spain international joined Chelsea for £8 million ($14.5 million) from Bilbao 12 months ago, but after failing to establish himself with the English club he is back on the market.
The 25-year-old has acknowledged Valencia's bid for his skills and but also admitted interest to return to his original side.
"I would love to return to the Primera Liga because it's a competition that I am very familiar with," Del Horno told Spanish newspaper Las Provincias.
"I am very honored by the interest from Valencia," he added.
Even with a move on the horizon Del Horno is remaining focused at his English premiership club.
"For the time being, though, my club is Chelsea and for that reason I have gone to pre-season training with them," he said.