The task is to open the brackets: I don't want these rumours (to spread) around. As far as I can see, both "to spread" and "to be spread" are possible. What sounds more natural to you? Does "around" influence your choice of Active/Passive?
Grammar books say we tend to use Active constructions. e.g. I have a lot of books to read. Exceptions to this rule are said to be: see (It remains to be seen) and do (There was nothing to be done about it).