In an interview with the Spanish newspaper AS, Alonso was quoted as saying that he was flattered to be linked with Real but would not request a move away from Anfield.
"It is always a great feeling when Madrid want you," he said. "Especially considering the phase of the career I am in now.
"But at this point, whether or not that can happen is not up to me. It's a matter that involves three parties, including myself. I do not like to force the issue. I prefer to talk."
Alonso's comments follow those of Real sporting director Miguel Pardeza, who said they are keen to add the Spain international to their squad for next season as president Florentino Perez continues his rebuilding at the Bernabeu.
He has already spent about £209m to bring some of the world's best players to the Bernabeu, including Brazilian playmaker Kaka, Portuguese forward Cristiano Ronaldo, French striker Karim Benzema and Spanish defender Raul Albiol.
One player who will is unlikely to move to Merseyside next season is Valencia striker David Villa.
The 27-year-old has been strongly linked with a move away from Spain this summer but Benitez ruled out any approach for the Spanish international.
We still have some time and we need to keep working on other names
Liverpool manager Rafael Benitez
"David Villa, he is not our target," he stressed.
But Benitez hinted there could be more arrivals in the summer, following the £17m capture of full-back Glen Johnson from Portsmouth.
"We have already signed Johnson, an international for England," he said.
"He is a good signing and Andriy Voronin is coming back (from a loan spell with Hertha Berlin), he was one of the best players in the German league, so we have two good additions. You never know in football, we still have some time and we need to keep working on other names.
"We have fantastic players and hopefully we can keep the level of last year and see with one or two additions we could improve a little bit. At the moment we are very pleased."
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