Big tech companies like Apple and Facebook are making moves into the global payments market — and fintech (financial technology) start-ups want to be part of the action. At the Money20/20 Europe conference in Amsterdam Monday, fintech firms positioned themselves as attractive partners, and possible takeover targets, for industry giants vying for a slice of the trillion-dollar global payments market. "Big tech has always been a very strong contender to actually come in and own parts of the financial services chain," said Rishi Khosla, co-founder and CEO of OakNorth, a U.K.-based digital bank that reached a $2.8 billion valuation earlier this year. Khosla added OakNorth is "in dialogue" with some tech companies over potential partnerships but wouldn't specify which ones by name.

In March, Apple unveiled its own credit card in combination with Goldman Sachs and Mastercard. Then in April, Uber secured a $500 million investment from PayPal ahead of its IPO (initial public offering). Meanwhile, Facebook is reportedly looking for partners to help develop its own cryptocurrency. Fintech CEOs told CNBC in Amsterdam that big tech firms are well-positioned to win over users thanks to their already-massive platforms. But that alone won't guarantee their success in payments or banking, they added. "We believe in the future whether it's the bank of Facebook, bank of Amazon, bank of Google, they're going to need to leverage that existing infrastructure," said Jason Gardner, CEO of Marqeta, a U.S.-based payments processor. "To go out and sort of replace that themselves would be incredibly difficult."

Gardner said Marqeta, which reached a $2 billion valuation last month, thinks of itself as the "engine room" by providing the "plumbing" for tech companies like Instacart and Square to process payments. He pointed to a wave of deals that have already taken place this year among payment firms, thanks to disruption from new fintech players. Last week, Global Payments and Total System Services agreed to a multi-billion dollar merger. In March, fintech group Fidelity National Information Services announced plans to buy Worldpay for roughly $35 billion. Some CEOs said they expect more consolidation as tech companies move into the sector. Michael Kent, CEO of U.K. payments start-up Azimo, said his company is "frequently approached" by companies looking to build out their payment capabilities. "Particularly in payments, scale matters," he said. "I think that will have a massive trickle-down effect towards the whole payments sector."