Django & WordPress - wp-admin redirect issue - django

Question

I have some specific configuration. I have a django site, and want to add an exiting blog which powered by Wordpress into django subfolder.
For security reasons I didn't want to install php stack aside django, and runned it in docker. Both are served by nginx, django also has a uwsgi.
In the Wordpress admin I configured both site and wordpress urls like this: https://mycoolsite.tld/blog
So, everything works well, except of some hardcoded redirect from https://mycoolsite.tld/blog/wp-admin to https://mycoolsite.tld/wp-admin.
The question - how can I play with nginx locations (and not tweak wordpress if possible) for accessing the /blog/wp-admin url?
Related nginx configs:
Django server - nginx blog location
location /blog/ {
rewrite ^/blog/(.*)$ /$1 break;
proxy_set_header X-Real-IP $remote_addr;
proxy_set_header X-Forwarded-For $remote_addr;
proxy_set_header Host $host;
proxy_pass http://127.0.0.1:8080; # localhost(8080) <--> docker(80)
proxy_redirect off;
}
Wordpress nginx config (inside docker):
server {
listen 80 default_server;
root /var/www/wordpress;
index index.php index.html index.htm;
location / {
try_files $uri $uri/ /index.php?$args;
}
error_page 404 /404.html;
error_page 500 502 503 504 /50x.html;
location = /50x.html {
root /usr/share/nginx/html;
}
location ~ \.php$ {
try_files $uri =404;
fastcgi_split_path_info ^(.+\.php)(/.+)$;
fastcgi_pass unix:/var/run/php5-fpm.sock;
fastcgi_index index.php;
fastcgi_param SCRIPT_FILENAME $document_root$fastcgi_script_name;
include fastcgi_params;
}
}