Morgan Stanley will offer rich clients access to three funds with Bitcoin exposure as soon as next month, making it the first large U.S. bank to do so.

The bank is making the move to meet demand from clients, unnamed sources with knowledge of the matter told CNBC

The funds offered are the Galaxy Bitcoin Fund, the Galaxy Institutional Bitcoin Fund and the FS NYDIG Select Fund.

Access to the cryptocurrency funds could be offered as early as next month, after the bank's financial advisers complete training on the new products, unnamed sources with knowledge of the matter told CNBC. 

Morgan Stanley will only offer the funds to clients with an "aggressive risk tolerance" and who hold at least $2 million in assets with the bank. Institutions seeking exposure to the funds need $5 million in assets. 

Qualifying Morgan Stanley clients are further restricted in their exposure to the Bitcoin funds. The bank will only allow them to invest 2.5% of their total net worth.

Morgan Stanley's move unlocks a significant new source of potential Bitcoin buyers. Its wealth management unit has 16,000 advisers and manages $4 trillion in assets, according to The Block.

Morgan Stanley clients must invest at least $25,000 in the NYDIG and Galaxy funds, while firms buying in to the Galaxy Institutional Bitcoin Fund must allocate at least $5 million. 

Clients at other big Wall Street banks are also asking for Bitcoin exposure. Goldman Sachs' chief operating officer John Waldron said last week that he sees client demand for Bitcoin rising, and that the bank continues to "evaluate and engage" on meeting that demand. The bank recently restarted a Bitcoin futures trading desk and is exploring an exchange-traded fund and custody service.