Hi  yogeshc,
Assign a JavaScript onclick event handler to the ActionLink.
Then, fetch the EmployeeId and set in the HTML Anchor tag.
Refer below example.
Database
For this example I have used of Northwind database that you can download using the link given below.
Download Northwind Database
Controller
public class HomeController : Controller
{
    // GET: Home
    public ActionResult Index()
    {
        NorthwindEntities entities = new NorthwindEntities();
        ViewData["Employees"] = entities.Employees.ToList();
        return View();
    }
}
View
@{
    Layout = null;
}
<!DOCTYPE html>
<html>
<head>
    <meta name="viewport" content="width=device-width" />
    <title>Index</title>
    <link rel="stylesheet" href="https://maxcdn.bootstrapcdn.com/bootstrap/3.3.2/css/bootstrap.min.css" />
    <script type="text/javascript" src="https://cdnjs.cloudflare.com/ajax/libs/jquery/3.7.1/jquery.min.js"></script>
    <script type="text/javascript" src="https://maxcdn.bootstrapcdn.com/bootstrap/3.3.2/js/bootstrap.min.js"></script>
    <script type="text/javascript">
        function GetSelectedId(link) {
            var id = $(link).closest('tr').find('td').eq(0).html();
            // Set the Id in Anchor link.
            $("#Selectclient").html(id);
            // Hide the modal.
            $("#exampleModal").hide();
            return false;
        }
    </script>
</head>
<body>
    <a href="#" class="col-md-5 col-form-label" data-toggle="modal" data-target="#exampleModal" id="Selectclient">Select Client</a>
    <div class="modal fade" id="exampleModal" tabindex="-1" role="dialog" aria-labelledby="exampleModalLabel" aria-hidden="true">
        <div class="modal-dialog modal-xl">
            <div class="modal-content">
                <div class="modal-header">
                    <h5 class="modal-title" id="exampleModalLabel">Select Client</h5>
                    <button type="button" class="close" data-dismiss="modal" aria-label="Close">
                        <span aria-hidden="true">×</span>
                    </button>
                </div>
                <div class="modal-body">
                    <div class="row">
                        <div class="col-lg-12 col-md-12 mb-12">
                            <div class="card">
                                <div class="card-body">
                                    <!-- <h5 class="card-title">Data Tabel</h5> --->
                                    <table id="dataTable" class="table table-striped table-bordered">
                                        <thead>
                                            <tr>
                                                <th>Employee Id</th>
                                                <th>First Name</th>
                                                <th>Last Name</th>
                                                <th>Country</th>
                                                <th>Select</th>
                                            </tr>
                                        </thead>
                                        <tbody>
                                            @foreach (var employee in ViewData["Employees"] as IEnumerable<Employee>)
                                            {
                                                <tr>
                                                    <td>@employee.EmployeeID</td>
                                                    <td>@employee.FirstName</td>
                                                    <td>@employee.LastName</td>
                                                    <td>@employee.Country</td>
                                                    <td>
                                                        @Html.ActionLink("Select", null, null, new { @onclick = "return GetSelectedId(this);" })
                                                    </td>
                                                </tr>
                                            }
                                        </tbody>
                                    </table>
                                </div>
                            </div>
                        </div>
                    </div>
                </div>
            </div>
        </div>
    </div>
</body>
</html>
Screenshot
