"We could not reach a definitive agreement. Euskaltel is now obliged, regrettably, to return to the process of an orderly and responsible closure of the project," they added.
"For Euskaltel and the team this is sad news after the hope generated by the initial agreement reached at the end of August and public declarations at that time by Alonso and his representatives."
Ferrari driver Alonso, a keen bike rider, had been set to purchase the company that owns the Basque team's WorldTour licence to enable them to continue racing in professional cycling's top league in 2014.
Led by Spain's Samuel Sanchez, the 2008 Olympic road-race champion, they face closure at the end of the season after 17 years of activity.
No financial details were given of Alonso's offer but Spanish media had reported that the double world champion had some six million euros (5.05 million pounds) available to spend on the project.
(Reporting by Braden Phillips, editing by Alan Baldwin)
