The BBC's global radio operation is understood to be facing an up to 25% reduction in its annual £272 million grant from the Foreign Office as part of wide-ranging public sector cuts.
In a speech to the Commonwealth Broadcasting Association in London, published in-full by the Press Gazette, Horrocks said that "careful thought must be given before Britain diminishes its voice in the global conversation".
Foreign secretary William Hague recently claimed that World Service will be protected from the worst of the cuts at the Foreign Office. However, there is concern that even a small budget cut could lead to a reduction in its operation, which covers 32 countries.
Horrocks said that World Service has implemented a series of efficiency drives that have delivered £74m of "cashable savings" since 1998, while still managing to grow its audience by a third to 42m people a week.
He also highlighted that the National Audit Office has placed World Service "in a minority of public bodies as having a 'good' track record on efficiencies".
Horrocks further pointed to the expansion being conducted by other countries of their global news services, such as China's $7bn overseas media operations programme and the $100m annual budget of the Al Jazeera English network, backed by the emir of Qatar.
Faced with the prospect of budget cuts, Horrocks said that he is wondering whether the World Service operation will be diminished "to a level where our presence is merely symbolic or lacking quality that damages our standing".
He said that he is also questioning whether World Service would be able to continue offering "lifeline services" during crises such as the Haiti Earthquake and Pakistan floods.
"These and many other questions are on my mind as we enter the final strait of our vigorous discussion about the future funding of the BBC World Service," he said.
"I can only hope that the answers are positive and that we can continue to deliver for the UK and continue to be the world’s leading broadcaster, a true partner for promoting independent media."