Aims: An efficient means of locating calibrator sources for international LOw Frequency ARray (LOFAR) is developed and used to determine the average density of usable calibrator sources on the sky for subarcsecond observations at 140 MHz. Methods We used the multi-beaming capability of LOFAR to conduct a fast and computationally inexpensive survey with the full international LOFAR array. Sources were preselected on the basis of 325 MHz arcminute-scale flux density using existing catalogues. By observing 30 different sources in each of the 12 sets of pointings per hour, we were able to inspect 630 sources in two hours to determine if they possess a sufficiently bright compact component to be usable as LOFAR delay calibrators. Results: More than 40% of the observed sources are detected on multiple baselines between international stations and 86 are classified as satisfactory calibrators. We show that a flat low-frequency spectrum (from 74 to 325 MHz) is the best predictor of compactness at 140 MHz. We extrapolate from our sample to show that the sky density of calibrators that are sufficiently bright to calibrate dispersive and non-dispersive delays for the international LOFAR using existing methods is 1.0 per square degree. Conclusions: The observed density of satisfactory delay calibrator sources means that observations with international LOFAR should be possible at virtually any point in the sky provided that a fast and efficient search, using the methodology described here, is conducted prior to the observation to identify the best calibrator.