You could shorten this even more if you did it in a single query, but since you say you must have two, here is a short version of your second query, with no need for the foreach loop:
$query = $this->db->query('
select `employee_id`, `ssn`, `first_name`,
`last_name`, `department`, `title`, `status`
from `employees` where `employee_id` = "'.$employee_id.'"');
return $query->result_array();
Using Active Records:
return $this->db
->select('`employee_id`, `ssn`, `first_name`,
`last_name`, `department`, `title`, `status`')
->where(array('employee_id' => $employee_id))
->get('employees')
->result_array();
UPDATE
Here is a short version with JOIN (replaces your whole code):
public function manager_list()
{
return $this->db
->select('e.employee_id, e.ssn, e.first_name,
e.last_name, e.department, e.title, e.status')
->join('managers AS m', 'e.employee_id = m.employee_id')
->where(array('e.employee_id' => $employee_id))
->get('employees AS e')
->result_array();
}