How to determine if a file descriptor is seekable?

Is there any portable way (on POSIX systems) to determine if a file descriptor is seekable? My thought is to use lseek(fd, 0, SEEK_CUR); and check if the return value is -1, but I'm uncertain if this could give false negatives or false positives. Using fstat and making assumptions about what types of files are seekable/nonseekable does not sound like a good idea. Any other ideas?