That's how we express wishes in English. wish + past simple (when talking about present and future) "I wish You were here" , "He wishes that he were rich" wish + past perfect (when talking about past) "They wish that they had studied harder when they were young."

I wish you were here. That is the correct form. Study it! When wishing for a different now: I wish + past tense...is the rule. Leann it. I wish I had a lot of money. I wish I had a big car. I wish I were somewhere else. I wish you didn't talk so much. When wishing for a future change in events, use "would". I wish you would shut up. I wish he would go away. I wish someone would give me a lot of money.

Мы в русском точно так же выражаем желания. Я хотел бы чтобы ты была (прошедшее время) здесь.

the key word in this sentence is "wish",if you want to describe something that isn't real or you may use this word . in the grammar book we call it Subjunctive Mood.（you can use wiki to find more things about Subjunctive Mood).and here ,this sentence means that the person in AL's songs is not by her side but AL think how nice if this person could be here.if use what you wrote,that's different,your sentence means AL hope this person will be here someday in the future(this in the grammar book we call it The Simple Future tense) wish my poor english could help you

The quoted sentence expresses the desire to share something nice with a person (for instance, it could be a sunset over a vast horizon), to have that person physically near, and to be able to communicate with she or he. For further details, I think Avril Lavigne could explain better; I ignore whether she is an Italki member.