Do I need footnotes in a Foreword if I cite something?
First, to make it clear, if you use something you need to cite it. I'm sure you agree with that. The question is about how to do the citation. 

For a book, I assume that there is an editor involved who will make decisions about such things as layout etc. If the book is being self-published by your colleague, then they might take on that task. But it is almost certainly someone besides yourself responsible for such things. 

Thus, I would submit your Foreword with complete citations. Whether inline or in footnotes is immaterial. But they need to be complete (not just referencing a book in general). The editor can then take what you give them and format appropriately. If you make them complete then the editor will have everything they need to do the job correctly. 

For what it's worth, I have seen footnotes in Forewords, but in a book length monograph, your length restriction seems rather short.