Best way to buy time on an exploding offer?

Hello all,

I am currently fortunate enough to have received a verbal offer in the FO at a large bank (pending background check), and an official written offer at another financial firm.

For reasons I do not want to disclose, I am leaning heavily to the FO position at the bank. However, I am in a big dilemma.

I have around 3 days preferably to sign the written offer. I like the company and job but it pales in comparison to the FO job. What is a good way to delay signing the current written offer until I get the official offer from my preferred job? Would contacting the hiring manager at the bank and telling him I have another offer and deadline, and emphasizing that I want to work at the bank preferably and would just need a timeline for when the contract will be sent, a bad idea?

Thank you so much for your help!