Answer
Wa `alaykum as-salamu wa rahmatullahi wa barakatuh.
In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
In this fatwa:
It is allowed to work for a non-Islamic bank as long as you don’t do any work related to riba contracts.
Responding to your question, Prof. Dr. Monzer Kahf, Professor of Islamic Finance and Economics at Qatar Faculty of Islamic Studies, states:
Yes, you can work in one of these banks provided you don’t do any of the following:
– Writing, preparing or typing an interest contract.
– Signing it on behalf of the bank.
– Be its witness.
The Prophet (peace and blessings be upon him) said that Allah’s wrath is on four in regards to riba: 1) taker, 2) payer, 3) writer and 4) its two witnesses.
However, although it is not haram, it is not one of good areas to work in because whatever you do in a conventional bank you will be helping riba.
Allah Almighty knows best.