SQL query for string in text which is not between quotes

I have an SQLite table which contains a 'text' column. I need to search this table for rows that have text containing a string (searchString) which is not between quotation marks. I also need it to be case-insensitive.

So:

text = blabla seARchString blabla "sEaRchString"

should pass the test but:

text = blabla "sEarchstring"

blabla should not

I have tried:

WHERE text GLOB *[^"]searchString[^"]*

But it is case-sensitive. I can't use REGEXP because android does not support it. Any ideas?