Is it allowed to keep budgies (small birds) at home in a cage or is it makrooh?
بسم الله الرحمن الرحيم
In the Name Of Allah, The Most Gracious, The Most Merciful
In Radd Al-Muhtar it’s stated that the ruling for keeping certain pets would be that it is permissible [mubah]. It is proven in al-Saheehayn that the brother of Anas ibn Maalik through his mother was called Abu ‘Umayr, and he had a bird whose name was al-Nughair. The bird died and the child grieved for it, and the Prophet (PBUH) tried to cheer him up by saying, “O Abu ‘Umayr, what happened to al-Nughayr?” The Nughair is a small bird. In conclusion, there should be no issue providing you do not cause harm to the bird and maintain it, as not doing so can incur sin. The life of all living things matter.
Only Allah knows best
Written by Maulana Moinul Abu Hamza
Checked and approved by Mufti Mohammed Tosir Miah
Darul Ifta Birmingham
 وَتَمْلِيكَ عُصْفُورٍ لِوَاجِدِهِ أَجِزْ Raddul Muhtaar, volume 6, page 477
 al-Bukhaari, 5778; Muslim, 2150