WPP bought a 13 per cent stake in the group in June, although it is prevented from launching a bid within a year.
City analysts said CIA was looking vulnerable, but added that a hostile takeover was out of the question as the agency's directors and employees owned almost 40 per cent of the shares.
Mr Sorrell also appeared to veto breaking up WPP, an idea he is believed to have considered earlier this year.
"We are seeking to make the sum of the group's parts greater than the individual businesses," he said.
WPP's interims came in at the top end of analysts' expectations. However, worries over the strength of sterling sent shares tumbling 7p to 266.5p in morning trading, although the stock recovered to close at 270p.
The share price fall could threaten Mr Sorrell's pay-out under a controversial incentive scheme. He stands to gain shares worth pounds 3m if the stock remains over the 265p "trigger", reached last week, for 60 days.
Under the five-year scheme, Mr Sorrell could earn a total of pounds 28m, including annual salary, bonuses and pension payments, if the share price reaches and maintains each target for 60 days.
Unveiling a 15 per cent increase in interim profits before tax to pounds 78.3m, Mr Sorrell admitted the company had put in a good performance, but said he was never happy and there was always more to achieve.
Mr Sorrell warned that the group still needed to co-ordinate its operations more effectively across the globe. "We have tremendous knowledge assets within the group that we are still failing to harness sufficiently," he said.
Mr Sorrell added that further co-operation was needed within the company's media buying and research divisions.
WPP's advertising agencies, J Walter Thompson and Ogilvy & Mather, were looking at merging their media buying and planning departments, he said.
Further small acquisitions remain likely and the announcement of a market research joint venture in China is expected imminently.
Emerging markets such as Asia-Pacific and Latin America were the most likely areas for future expansion, the company said.
WPP has bought back pounds 22m worth of shares this year and Mr Sorrell said that a similar buy-back was "highly possible" next year.