The firm, one of only two of America's "big five" business-to-business banks still standing, seems set to make the sale to China Investment Corporation (CIC), a state-owned fund.
A potential alternative to this deal, however, is also being discussed by executives at Morgan - with North Carolina-based Wachovia reportedly interested in a tie-up.
CIC currently retains around $200 billion of assets, and bought a 9.9 per cent stake in Morgan for $5 billion in December 2007.
Financial stocks have been battered on the markets over recent days, with investor confidence in the sector declining on news of Lehman's bankruptcy and Merrill's merger.
However, a recovery is likely to be staged when the markets open later today, with reports of government plans for a fund to buy up banks' bad debts and a temporary ban on shorting stocks.
Morgan refused to comment on the takeover and merger talks.
However, a spokesperson said that the firm was "focused on solutions" to its current financial woes.
Morgan shares closed at $22.55 yesterday - a fraction of their pre-credit crunch price.