Not quite sure what you're trying to do but maybe something like:
PHP Code:
$query ="SELECT entryid, entrytext,";
$query.=" DATE_FORMAT(entrydate, '%M %d, %Y %T') AS date";
$query.=" FROM blog ORDER BY entrydate DESC LIMIT 10";
$query.=" WHERE MONTHNAME(date) = '$required_month'";
$result=mysql_query($query);
Is that what you were getting at?