PayPal has long been both a friend and a foe to credit card companies. But to Visa CEO Charlie Scharf, it's either one or the other.

At a tech conference hosted by JPMorgan Chase this week, Scharf said he wants PayPal to stop urging its users to fund their PayPal accounts with their bank accounts — a method called ACH — instead of debit or credit cards. Such an arrangement is more profitable for PayPal, but a problem for card companies like Visa.

I've been very, very clear on this one which is if you are a foe, you're not a friend. And PayPal's historic model, on the one hand, 50% of the volume is ACH, the other 50 percent is general purpose cards of which we're half of it. So, they drive a lot of business our way. That's supposedly the friend part of it. The foe part is where they then use historically those transactions to do everything they can to get those to ACH where we and our clients get disintermediated from the transaction, the entire experience, and it causes tremendous customer service problems for the bank specifically.

He wasn't done.

And so, anyone that's trying to take your customers and disintermediate you is not a friend. And so, that's the reality of the way we viewed PayPal historically. And so, we've said, listen, historically, they were the only game in town. But as we just talked about, there are lots of other opportunities for us to capture that share. We'd love to figure out a different model with them where it's consumer choice first whether or not disintermediating. If we can figure that out with them, great. We'll think of them more as a partner. They need to do things differently in order to do that. The other door is where we go full steam and compete with them in ways that people have never seen before. Because you've never seen us go target PayPal in the marketplace in any meaningful way.

Whoa boy. Emphasis mine on those last two sentences.

Scharf went on to say that those words shouldn't be construed as a threat, but that's sure what they sound like.

What would increased competition with PayPal look like for Visa? According to a note Autonomous Research partner Craig Maurer sent to clients, it could be several things.

Visa could get more aggressive with the rollout of its Visa Checkout payment method for e-commerce websites. It could step up promotion of Apple Pay and Android Pay, which don't work with PayPal. And it could give discounts on transaction fees to companies that use things like fingerprint technology to make payments more secure — again, something PayPal doesn't do.

"In conclusion," Maurer wrote, "we continue to believe that investor expectations for a grand bargain between PayPal, Visa and MasterCard need to be shelved for at least the near-term, if not longer."