In fact it is a Latin word:
From Latin aspīrāre = to breathe upon, pant after, a- +spīrāre = to breathe, to blow
Dictionary.com Unabridged
Based on the Random House Dictionary, © Random House, Inc. 2011
To long, aim, or seek ambitiously;
be eagerly desirous, especially for something great or of high value
(usually followed by to, after, or an infinitive):
to aspire after literary immortality; to aspire to be a doctor.