The Madrid prosecution office announced on Wednesday it was seeking the sentence for an alleged fraud of €2 million between 2010 and 2012.
It is claimed Alonso used a company based on the Portugese island of Madeira to avoid declaring income earned from the 36-year-old's image rights.
As well as the five-year imprisonment, a fine of €4 million is held against Alonso, his tax advisor Ivan Zaldua and the manager of the Portuguese company, Ignasi Maestre.
The prosecution also demands the return of the sum denied to the Spanish tax office, in addition to any interest gained.
The Madrid court in charge of the investigation reopended the case at the end of 2017 after the judges on appeal found the facts alleged against Alonso were "sufficiently substantiated".
Alonso, who retired last year, is not the first high-profile footballer to have faced problems over Spanish tax in recent years.
Some have admitted fraud in exchange for a sentence to avoid jail, like Manchester United forward Alexis Sanchez, former Barcelona midfielder Javier Mascherano and Real Madrid defender Marcelo.
Barcelona's Lionel Messi was sentenced to a fine of €2.1 million for tax evasion and a sentence of 21 months in prison, subsequently issued as a fine.
Real Madrid striker Cristiano Ronaldo is also charged with alleged fraud of €14.7 million, which he denies.