Cable & Wireless Worldwide shareholder Orbis said it would be prepared to retain its 19 percent stake in the corporate telecoms company if Vodafone took control.

The investor said on Monday that Vodafone's agreed 38 pence-a-share offer undervalued CWW's assets and it declined to publicly back the deal.

Certainly the prospect of being a shareholder in a stand-alone or Vodafone-led CWW are two potential outcomes Orbis has planned for and is comfortable with, a spokesman said on Tuesday.

Vodafone has the endorsement of CWW's directors and the holders of 18.6 percent of the stock for its offer, which is structured with a scheme of arrangement requiring acceptances from the holders of 75 percent of the shares.

But Vodafone retains the option of changing the deal to a takeover structure, whereby it sets a threshold above 50 percent, according to its statement.

A Vodafone spokesman declined to comment on whether the group could change the structure of the deal.

The mobile phone giant, however, prefers full ownership of its subsidiaries and has been selling off stakes in companies where it does not have full control.

(Reporting by Paul Sandle; Editing by Helen Massy-Beresford)