Some months ago I received a rejection that I thought was a bit nicer than the average bland "does not fit …". Recently I re-read it. The publishers stated that if I "significantly revised" the manuscript I was welcome to re-submit it after six months, and that they hoped I would consider them for my next project. My question is, does this actually mean anything or is it just a polite formula, as I first understood it. And if they are suggesting I revise it, how do I know what they would like me to change (if I can)? Would it be acceptable to ask them this question, especially as there has been a time interval of a few months? (They may have totally forgotten what the manuscript was all about!)
When I reject things I certainly don't invite people to resubmit unless I mean it - for one thing, I'm not so desperate for people to like me that I'll give writers hope that one day I may reconsider my rejection of them if only they'd comply with my mysteriously absent feedback on their manuscript ...
So this publisher meant it. And they also meant they'd like to see what you write next (I make the same offer on occasion and I always mean it, but I certainly don't say it to everyone).
However, just because they asked you to revise the manuscript doesn't mean that they'll give you any pointers on how to do that. The main reason for this is that it can several hours to write a manuscript report and there's no guarantee that the writer will take any of it into account when writing the next draft. No one at a publishing company, or agency, has time for that. So this publisher likely hopes that you have your own methods of working out what to revise. Time is a good method (I'm being serious) - leaving a draft alone for a while can make it so much clearer when you return to it, and sometimes that bit of distance is all the writer needs in order to assess what should be changed. Some writers seek advice from other writers or from editors.
By all means contact them and say that you're willing to revise but you'd really appreciate any guidance they can give - just don't be surprised if they don't give it, for the reasons mentioned above. And also consider leaving this manuscript alone for quite a while as you get on with that next manuscript they have already said they'd like to see.