The playmaker is hoping to get his hands on the prestigious trophy this season under Jose Mourinho, and has also expressed a desire to return to Real Sociedad one day
The 28-year-old still has not experienced winning a championship, despite featuring for the likes of Madrid and Liverpool during his illustrious career.
"I need a league, I wish to touch the trophy this year," Alonso told Spanish sports daily Marca. "I have been runner-up with Liverpool and again for two years in Madrid, it's time to get it."
The capital outfit enjoyed a reasonably successful 2010-11 campaign, winning the Copa del Rey from the hands of Barcelona, but failed to catch up with their Catalan counterparts, who won a third consecutive league title and another Champions League trophy, and admits they are worthy champions.
"They have very good players, and have consolidated in recent times," he continued. "They have enjoyed three years of outstanding results but Real Madrid will compete."
Alonso also touched on the possibility of ending his career with Real Sociedad, his first ever club, but remained coy on the prospect on returning to San Sebastian any time soon.
He said: "Ideally it would be nice to go home one day, but my intention is to continue here."