I agree with @mtj's answer : YAGNI, no point in making the string reusable if it's not being reused at the moment.
I would want to add that in certain scenarios it may be smart to factor out only part of the SQL query.
For example if you had a few queries with slightly more complicated WHERE statements, something like :
select * from image where (created_date is null or created_date > date)
and
select id from text where (created_date is null or created_date > date)
Then we can have
private static String WHERE_CREATED_IS_NULL_OR_AFTER_DATE = " where (created_date is null or created_date > date) "
and use it in the respective methods :
public void getImages() { String query = "select * from image"+ WHERE_CREATED_IS_NULL_OR_AFTER_DATE; ...}
public void getTextIds() { String query = "select id from text"+ WHERE_CREATED_IS_NULL_OR_AFTER_DATE; ...}