How to store Private Key in Browser

I am trying to create a delegate wallet for every user which is connected to my dApp. I intend to have access to the private key so that I can initiate and sign transactions on the users behalf.

So I am thinking of making the wallet pub and priv key on client side and I don't want the priv key to ever leave client's browser.

Is it possible to implement something like this ?

I use Privy for siwe if that can help me in any way.