Alonso’s former club, Liverpool and Chelsea were linked with moves for the Spanish international, who has just 12 months remaining on his current deal at Real Madrid.
The 31-year-old had an impressive five-year spell at Anfield between August 2004 and August 2009, establishing himself as one of the stand-out midfielders in the Premier League.
He reportedly turned down a two-year extension to his contract at the Bernabeu last year, but seems intent on seeing out the final year of his deal.
This is despite the fact that the 31-year-old was supposedly unhappy with the atmosphere at Madrid and seemed keen on a move away just over a month ago.
“The Premier League? No,” Alonso said, when asked about a Premier League switch.
“No way, no chance.”
Jose Mourinho was rumoured to be keen to take the player with him to West London, in his second term as Chelsea manager.
Alonso has yet to be offered a new contract this summer, despite being a mainstay in the Real Madrid side last season, making 47 appearances in all competitions.
The signing of Asier Illarramendi from Real Sociedad means his first-team opportunities could be more limited in the upcoming season.