This is a sentence taken from a job application written by a friend of mine. I think the word grant is not correct here but I don't know which word would be better here.

I thank you very much for considering my application and hope you will grant me an interview.

Thanks for your help.
I see nothing wrong or inappropriate in "grant me an interview".

Merriam-Webster: GRANT implies giving to a claimant or petitioner something that could be withheld.
Interesting; "...grant me an interview..." googles, but it seems somewhat sarcastic, in this context – to my ear, anyway. (Or maybe too humble?)

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Grant is not the word to use here or at least not the best choice. ... and hope you will give/offer me an interview.

Dear Coachpotato,

It is not normal to say «I hope you will grant me an interview». It is better to say «offer me an interview». Emotion: smile

It is however in my opinion inappropriate. Your friend should say «Thank you very much for considering my application. I look forward to hearing from you.»

Kind regards, Emotion: smile

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