That would defeat the purpose of bitcoin being a decentralized currency. What is possible is for banks to create a new product, somehow similar to bitcoin and offer it as another investment. Or they could just offer this new service to their online banking client as another added value service. But bitcoin as is being used by banks to be offered should destroy it altogether.
People tend to forget that bitcoins key role is that is it decentralized, with other words it's not owned by a single person or company. the moment several large entities hold many bitcoin they will be holding to much coins and that's not positive for bitcoin. Especially since we want to keep using it privately.