The 29-year-old moved to the Spanish outfit at the start of the season and has scored 10 times during a successful first season in Madrid.
The experienced forward's current deal is due to expire this summer, but he is hopeful of penning fresh terms, despite reported interest from Deportivo La Coruna.
"If Rayo wants me to stay for another year, I for one would be delighted. I wish that would happen. I'm happy in this team and enjoying myself on and off the pitch," Inside Spanish Football quotes the Argentine as saying.
Larrivey started his professional career with Argentine side Huracan.