The client has given me a design which has a Select Option menu containing a checkbox together with the item name as individual items in the list. Is there anyway possible to add a checkbox inside a Select Option menu?

NB: Developer needs to add his own id to make the menu effective, I only need the HTML CSS code if it is possible.

For a Pure CSS approach, you can use the :checked selector combined with the ::before selector to inline conditional content.

Just add the class select-checkbox to your select element and include the following CSS:

<!-- language: lang-css -->
.select-checkbox option::before {
  content: "\2610";
  width: 1.3em;
  text-align: center;
  display: inline-block;
}
.select-checkbox option:checked::before {
  content: "\2611";
}

You can use plain old unicode characters (with an escaped hex encoding) like these:

Or if you want to spice things up, you can use these FontAwesome glyphs

Screenshot

Demo in jsFiddle & Stack Snippets

<!-- begin snippet: js hide: true console: true babel: false --> <!-- language: lang-css -->
select {
  width: 150px;
}

.select-checkbox option::before {
  content: "\2610";
  width: 1.3em;
  text-align: center;
  display: inline-block;
}
.select-checkbox option:checked::before {
  content: "\2611";
}

.select-checkbox-fa option::before {
  font-family: FontAwesome;
  content: "\f096";
  width: 1.3em;
  display: inline-block;
  margin-left: 2px;
}
.select-checkbox-fa option:checked::before {
  content: "\f046";
}
<!-- language: lang-html -->
<link rel="stylesheet" type="text/css" href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/4.7.0/css/font-awesome.css">

<h3>Unicode</h3>
<select multiple="" class="form-control select-checkbox" size="5">
  <option>Dog</option>
  <option>Cat</option>
  <option>Hippo</option>
  <option>Dinosaur</option>
  <option>Another Dog</option>
</select>

<h3>Font Awesome</h3>
<select multiple="" class="form-control select-checkbox-fa" size="5">
  <option>Dog</option>
  <option>Cat</option>
  <option>Hippo</option>
  <option>Dinosaur</option>
  <option>Another Dog</option>
</select>
<!-- end snippet -->

Note: Beware of IE compatibility issues however