Solution

• In Controller Class,
  • Initialize your Future Method as your Model : Future<List<LeaveModel>> getLeaves(){}
  • create a List of Obj for Custom Class like this :
    List<LeaveModel> leaveTypeObjList = [];
  • After fetching data from API add the datas in obj list via Object

type :LeaveModel leaveTypeObj = LeaveModel(leaveTypeResponseList[i]["LEAVE_TYPE_EN"]);

• And in loop add it to your obj list: leaveTypeObjList.add(leaveTypeObj);

** In widget class at AsyncSnapshot use your List of Generics like this :
AsyncSnapshot<List<LeaveModel>>.

Demo Code

import 'dart:convert';

import 'package:flutter/material.dart';
import 'package:http/http.dart' as http;

void main(List<String> args) {
  runApp(MyHome());
}

class MyHome extends StatelessWidget {
  const MyHome({super.key});

  @override
  Widget build(BuildContext context) {
    return MaterialApp(
      home: MyApp(),
    );
  }
}

class MyApp extends StatefulWidget {
  const MyApp({super.key});

  @override
  State<MyApp> createState() => _MyAppState();
}

class _MyAppState extends State<MyApp> {
  List<String> leaveTypeList = [];
  int currentLeaveType = 0;
  String? value;
  String? selectedLeaveType;
  late Future<List<LeaveModel>> futureLeaves;

  @override
  void initState() {
    super.initState();
    futureLeaves = FoodTypeController().getLeaves();
  }

  @override
  Widget build(BuildContext context) {
    return Scaffold(
      body: Container(
        height: double.infinity,
        width: double.infinity,
        child: Row(
          children: [
            Text(
              "Leave Type =   ",
              style: TextStyle(fontSize: 24.0),
            ),
            FutureBuilder(
                future: futureLeaves,
                builder: ((BuildContext context,
                    AsyncSnapshot<List<LeaveModel>> snapshot) {
                  if (snapshot.hasData) {
                    leaveTypeList = [];
                    List<LeaveModel>? LeaveTypes = snapshot.data;

                    for (int i = 0; i < LeaveTypes!.length; i++) {
                      leaveTypeList.add(LeaveTypes[i].leaveTypes!);
                    }

                    return SizedBox(
                      width: 200,
                      height: 50,
                      child: Container(
                        padding: EdgeInsets.only(left: 2.0, right: 4.0),
                        decoration: BoxDecoration(
                            borderRadius: BorderRadius.circular(20),
                            border: Border.all(color: Colors.black, width: 1)),
                        child: DropdownButtonHideUnderline(
                          child: DropdownButton<String>(
                            borderRadius: BorderRadius.circular(12),
                            value: currentLeaveType == null? null: leaveTypeList[currentLeaveType],
                            icon: Icon(Icons.arrow_drop_down_rounded),
                            items: leaveTypeList.map(buildMenuItem).toList(),
                            onChanged: (value) => setState(() {
                              currentLeaveType = leaveTypeList.indexOf(value.toString());
                              this.value = value;

                              selectedLeaveType = this.value;
                            }),
                          ),
                        ),
                      ),
                    );
                  } else if (snapshot.hasError) {
                    return const Text("Error to load Snapshot");
                  } else {
                    return const CircularProgressIndicator();
                  }
                })),
          ],
        ),
      ),
    );
  }

  DropdownMenuItem<String> buildMenuItem(String item) => DropdownMenuItem(
        value: item,
        child: Text(
          item.toString(),
          style: TextStyle(fontWeight: FontWeight.w400, fontSize: 24.0),
        ),
      );
}

class LeaveModel {
  String? leaveTypes;
  LeaveModel(this.leaveTypes);
}

class FoodTypeController {
  Future<List<LeaveModel>> getLeaves() async {
    List<LeaveModel> leaveTypeObjList = [];

    String url = "";

    http.Response response =
        await http.post(Uri.parse(url), body: {"user": "", "pass": ""});

    if (response.statusCode == 200) {
      List leaveTypeResponseList = jsonDecode(response.body);

      for (int i = 0; i < leaveTypeResponseList.length; i++) {
        LeaveModel leaveTypeObj =
            LeaveModel(leaveTypeResponseList[i]["LEAVE_TYPE"]);
        leaveTypeObjList.add(leaveTypeObj);
      }
      return leaveTypeObjList;
    } else {
      throw Exception("Error to load data in Leave Controller");
    }
  }
}

Response

Visual