Why don’t you try with ViewModel, and SelectListItem? I would do something like this
Controller:
Model.Employees = employeesList.Select(employee => new SelectListItem
{
Text = employee.FullName,
Value = employee.Id
}).ToList();
HTML:
@Html.DropDownListFor(m => m.EmployeeId, new SelectList(Model.Employees, "value", "text"))
EmployeeId should be string. And then you just need to set EmployeeId.