Passing attributes to shortcode dynamically

Not quite like that, but you can achieve the same result if you use a pre-defined value or argument in your shortcode to act as a “flag”:

[authoorsposts author="post"]

…then in your handler:

function wpse_209684_author( $atts ) {
    if ( ! empty( $atts['author'] ) ) {
        $author = $atts['author'];

        if ( $author === 'post' ) // Our flag, make $author the current post author
            $author = get_the_author_id();
        else // Otherwise just accept a hardcoded author ID
            $author = absint( $author );
    }
}