Here is how the New York Times framed the invitation:
He [Jin Liquan] is not giving up on the United States, even if his chances are remote. "We have a standing invitation" for the United States to join the bank, Mr. Jin said, during an appearance at the Brookings Institution. "Anytime you think you are ready, pick up the phone, give me a ring."
He made the comment at this event at Brookings.
Here is what Brookings scholar David Dollar has written about the AIIB. Here is what Brookings scholar Jonathan Pollack says about how the US will respond to AIIB's expanding membership. Here is what Brookings scholar Thomas Wright says about AIIB. And here is what Brookings fellow Philippe Le Corre says about AIIB.