Display Value of BD in SELECT in PHP

Inside the while it analyzes the value that the user has; assuming it is idnivel:

while($row2 = $result2->fetch_array())
{
    $sel = ($row['idnivel'] == $row2['id']) ? ' selected' : '';
    echo "<option value=\"{$row2['id']}\"$sel>{$row2['nivel']}</option>";
}

If you are not working with HTML5 then instead of 'selected' you should put 'selected="selected"'.

Remember that all HTML tags (regardless of the version) and their attributes must be written in lowercase.

This is my proposal, taking into account what has been said in my comments.

I omitted the second SELECT, because I understood that it was not necessary for the purposes of your program. You may also consider selecting fewer fields in your SQL query, if you are not going to need them.

<form name="fe" action="" method="post">
        <table border="2">
            <tbody><tr><td>Nombre de Usuario</td>
            <td><input name="txtbus" type="text"></td>
            <td><input name="btn1" value="Buscar" type="submit" onsubmit="this.reset()"></td></tr>
    </form>
<?php
$btn = "";
if(isset($_POST["btn1"])){
    $btn=$_POST["btn1"];
    $bus=$_POST["txtbus"];

    if($btn=="Buscar"){

        require_once('config.php');
        $mysqli = mysqli_init();
        $mysqli->options(MYSQLI_OPT_CONNECT_TIMEOUT, 5);
        $mysqli->real_connect($config['db_host'],$config['db_user'],$config['db_password'],$config['db_name']);

        if ($mysqli){
            $queryM = 
                    "SELECT u.nombre_usuario, u.nombre, u.idnivel, s.idservicio, 
                            e.idestado, s.servicio, e.estado, n.nivel
                      FROM usuario u 
                      INNER JOIN servicio s ON u.idservicio = s.id 
                      INNER JOIN estado e ON u.idestado   = e.id
                      INNER JOIN nivel n ON u.idnivel    = n.id
                      WHERE u.nombre_usuario = ?
                      ORDER BY u.id";
            $stmt=$mysqli->prepare($queryM);
            if ($stmt){

              $stmt->bind_param("s",$bus);
              $stmt->execute();
              $stmt->bind_result($nombre_usuario, $nombre, $idnivel, $idservicio, $idestado, $servicio, $estado, $nivel);   
?>  
            <form class='contacto'>
            <div><etiqueta>Nombre de Usuario:</etiqueta><input type='text' value='<?php echo $row['nombre_usuario']?>'></div>
            <div><etiqueta>Empleado:</etiqueta><input type='text' value='<?php echo $row['nombre']?>'></div>
            <div>
                <etiqueta>Nivel</etiqueta>
                <select id="nivel" name="nivel">
<?php 
              while ($stmt->fetch()) {
                    echo "<option value=\"$idnivel\">$nivel</option>";
              } 
              $stmt->close();
?> 
            </select>   
            </div>
            <div><etiqueta>Tipo de Servicio:</etiqueta><input type='text' value='<?php echo $row['servicio']?>'></div>
            <div><etiqueta>Estatus:</etiqueta><input type='text' value='<?php echo $row['estado']?>'></div>
            <!--<div><label>Estatus:</label><textarea rows='6'></textarea></div>-->
            <a id="cancelupdate" class="button delete" onsubmit="this.reset()">Cancelar</a>
            <div><input type='submit' value='Envia Mensaje' onsubmit="this.reset()"></div>
        </form>
<?php
      }else{

          echo "Error en la consulta SQL";

      }
              $mysqli->close();

}else{

        echo "No se pudo conectar a la base de datos";  
}

    }else{

        echo "Opción buscar no fue seleccionada"; //Esta comprobación se puede omitir o cambiar por otra cosa

    }

}else{

    echo "btn1 no presionado";

}