The 32-year-old recently signed a new contract with the Spanish giants that will see him stay at the Santiago Bernabeu until June 2016.
Alonso, who moved to Madrid from Liverpool in 2009, claims that he does not discount the notion that he could move to the USA or return to his first club Real Sociedad.
"Moving to the USA? I don't reject that in the future," he told France Football.
"We will see how I feel in two years' time. I don't discount anything - Europe, Real Sociedad or staying longer at Real Madrid if I notice that I still have the physical abilities."
Alonso has also insisted that he made the right decision to switch to Madrid after five years at Liverpool during which time he won the FA Cup and the Champions League.
"In 2009, I think I made the right decision," said the Spain international. "After five years at Liverpool, I needed a change.
"Can you expect anything better than Real Madrid, the greatest and most demanding club? It was the right moment to seize the opportunity.
"Everyday life in Madrid is tougher than in any other team. What the club demands is win, win and win again, and play well too.
"Liverpool have five European trophies, but it is not the same. There the daily life is more relaxed and not so heavy. At Real, pressure and demand are constant.
"But I wanted to see if I could match such a challenge."