Ayala’s contract with the Spaniards expire at the end of the season and the 36-year-old Argentine is looking to head home.
“I have said that I would like the challenge, but we will see what happens,” he told Ole.
“Going to River would be great. (Chairman Daniel) Passarella has called me and I was pleasantly surprised to hear that River are interested.
“I was not able to enjoy my experience there as much as I would like last time, but the club opened the door to Europe for me and I will always be grateful to them.”
Ayala admits he would be happy to work with Passarella again at River.
“(Coach) Leo Astrada knows me and knows what I can offer,” he added.
“The same is true of Passarella, as he took a chance on me during my first spell with River and with the national team.
“There is nothing formal yet, but I like the idea.
“The interest is there and we will see what happens. I am committed to Zaragoza until June, I am under contract, but after that we’ll see.”
