Run HTTP server aiohttp inside of your discord bot to handle HTTP requests. Cog based example.

http_cog.py

from aiohttp import web
import asyncio
import discord 
from discord.ext import commands

class HTTPCog(commands.Cog):

    def __init__(self, bot):
        self.bot = bot

    async def webserver(self):
        async def handler(request):
            print("hehe")
            return web.Response(text="Hello, world")

        async def post_handler(request):
            print(await request.json())
            return web.Response(text="post request")

        app = web.Application()
        app.router.add_get('/', handler)
        app.router.add_post('/', post_handler)
        runner = web.AppRunner(app)
        await runner.setup()
        self.site = web.TCPSite(runner, '127.0.0.1', 8080)
        await self.bot.wait_until_ready()
        await self.site.start()

    def __unload(self):
        asyncio.ensure_future(self.site.stop())

def setup(bot):
    http_cog = HTTPCog(bot)
    bot.add_cog(http_cog)
    bot.loop.create_task(http_cog.webserver())

For prior discussion refer to this gist https://gist.github.com/Peppermint777/c8465f9ce8b579a8ca3e78845309b832