As you posted no code and little in the way of exactly what criteria you are using, I can’t really writ functioning code but inside your Loop try:
var_dump($posts[$wp_query->current_post -1]->post_title);
That is, $posts[$wp_query->current_post -1] is the previous post. You can change -1 to plus or minus whatever value you want but the math cannot result is a figure below 0 or above your posts_per_page -1 (I think), as those don’t exist. The query only gets posts on “this page”. If you do need information from posts that appear on a previous or next page you will have to query for that information.