The defender, who scored a rare goal on Wednesday as los Blancos romped into the last 16 of the Champions League, also had words of praise for coach Carlo Ancelotti
Alonso has only recently recovered from an injury that saw him miss the start of the season and has been slowly blending back into a Blancos midfield that will now be without Sami Khedira for the next six months.
However, Arbeloa does not believe there is a more influential player in world football and feels that his fellow Spain international should ignore interest from elsewhere to remain at the Santiago Bernabeu beyond the end of the season.
"Xabi Alonso is my friend," the full-back told Canal Plus. "We depend on him a lot. There is no player in the world able to influence more on the team than him.
"Xabi won't be better anywhere else than he is here."
Madrid - without the injured Cristiano Ronaldo - had to play with 10 men for most of their Champions League clash with Galatasaray on Wednesday night, after Sergio Ramos was sent off in the first half, but goals from Gareth Bale, Arbeloa, Angel Di Maria and Isco rendered Umut Bulut's goal obsolete.
Arbeloa scored the first of three second-half strikes from the Blancos and he credited both coach Carlo Ancelotti and the Bernabeu faithful for their much improved performance after the break.
"The second half was great," the full-back added. "The coach did it with his tactical changes.
"Today I'm grateful for the fans' support - they know how that we don't compensate on work or effort."
Madrid's victory ensured that they will progress to the last 16 as winners of Group B.