yes there will probably be discounts for an onsite stay at DLP for June - depending on how many nights you are looking to stay there may be offers already on sale. Check the UK version of the DLP site, plus others (France, Netherlands etc etc) to see what offers, if any, are out there for your dates.
If there are no decent offers, then hang on in there and keep looking - they'll turn up eventually. No-one knows what offer will come out, its just a case of looking at the price and seeing if that price suits you. Generally speaking, I look for a 40% off full price or equivalent (so if staying 4 nights, 2 nights free for example), and consider that a fair price for DLP onsite hotel packages.
Also, you might want to consider offsite but nearby - there is loads of accommodation in the resort area. Then you could get your own park tickets or annual passes.