Use menu link or onClick to set a variable

By this you can pass the value using ajax, you have fetch value from $_POST in your php script

jQuery(document).ready(function(){
  jQuery('.dayLink a').click(function(){
     var li_id = jQuery(this).closest('.dayLink').attr('id');
     jQuery.ajax({
        url: 'url_to_php_script',
        data: {dayValue: li_id,action:call_to_ajax},
        method: 'POST',
        success: function(res){
            console.log(res);
        }
     })
  });
});

The closing brackets were out of order.

<?php
if(isset($_GET['li_id'])){
    $test = $_GET['li_id'];
    echo $test;
    }
?>

New php script added to echo the value passed with the POST method.

Below is the entire script in the php file.

<script type="text/javascript">
jQuery(document).ready(function(){
  jQuery('.dayLink a').click(function(){
  var li_id = jQuery(this).closest('.dayLink').attr('id');
  jQuery.ajax({
    url: 'https://grat-itudefitness/wp-content/themes/divi-child-gratitudefitness/includes/b2p_program_navigation.php',
    data: {dayValue: li_id},
    method: 'POST',
    success: function(res){
      console.log(res);
      }
    })
  });
});
</script>

<?php
if(isset($_GET['li_id'])){
  $test = $_GET['li_id'];
  echo $test;
  }
?>

<!-- Exercise Menu -->
<ul class="topnav" id="myTopnav">
  <li class="dayLink" id="day_1"><a href="https://wordpress.stackexchange.com/questions/254179/javascript:void(0)">Day 1</a></li>
  <li class="dayLink" id="day_2"><a href="https://wordpress.stackexchange.com/questions/254179/javascript:void(0)">Day 2</a></li>       
  <li class="dayLink" id="day_3"><a href="https://wordpress.stackexchange.com/questions/254179/javascript:void(0)">Day 3</a></li>
  <li class="dayLink" id="day_4"><a href="https://wordpress.stackexchange.com/questions/254179/javascript:void(0)">Day 4</a></li>
  <li class="dayLink" id="day_5"><a href="https://wordpress.stackexchange.com/questions/254179/javascript:void(0)">Day 5</a></li>
  <li class="dayLink" id="day_6"><a href="https://wordpress.stackexchange.com/questions/254179/javascript:void(0)">Day 6</a></li>
  <li class="dayLink" id="day_7"><a href="https://wordpress.stackexchange.com/questions/254179/javascript:void(0)">Day 7</a></li>
</ul>

The code you need::

** Code to keep in template file **

<?php
  $actionName="callMyAjax";
  $nonce = wp_create_nonce($actionName);
?>
<script type="text/javascript">
jQuery(document).ready(function(){
  jQuery('.dayLink a').click(function(){
  var li_id = jQuery(this).closest('.dayLink').attr('id');
  jQuery.ajax({
    url: 'https://example.com/wp-admin/admin-ajax.php',
    data: {dayValue: li_id,action:<?php echo $actionName; ?>,ajaxOrigin:<?php echo $nonce; ?>},
    method: 'POST',
    success: function(res){
      console.log(res);
      }
    })
  });
});
</script>

** Code to keep in Functions **

<?php
function myAjaxHanlder()
{
  if(isset($_POST['ajaxOrigin']) && wp_verify_nonce($_POST['ajaxOrigin'], 'callMyAjax')){
    if(isset($_POST['li_id'])){
      $test = $_POST['li_id'];
      echo $test;
    }
  }
}
add_action('wp_ajax_callMyAjax', 'myAjaxHanlder' );
add_action('wp_ajax_nopriv_callMyAjax', 'myAjaxHanlder' );
?>