Doesn't work on Windows, works on Linux and maybe OS X.

requests_bind_to_interface.py

import socket
import requests
from requests.adapters import HTTPAdapter
from requests.packages.urllib3.poolmanager import PoolManager


class SourceInterfaceAdapter(HTTPAdapter):
    def __init__(self, source_interface, **kwargs):
        self.source_interface = source_interface

        super(SourceInterfaceAdapter, self).__init__(**kwargs)

    def init_poolmanager(self, connections, maxsize, block=False):
        self.poolmanager = PoolManager(
            num_pools=connections,
            maxsize=maxsize,
            block=block,
            socket_options=((socket.SOL_SOCKET, 25, str(self.source_interface + '\0').encode('utf-8')),)
        )

s = requests.Session()
s.mount('http://', SourceInterfaceAdapter('eth0'))
s.mount('https://', SourceInterfaceAdapter('eth0'))

r = s.get('https://ifconfig.co/', headers={'User-Agent': 'curl/7.61.0'})
print(r.text)