Strictly speaking you are allowed to buy players whenever you want, you just can't register them until 1st January and the day after the domestic season finishes. That is why the date is being shown as 25th May for Premier League but FL clubs are buying players now e.g. Cardiff have just bought the Norwich goalie.
Bear in mind though that the Italian, Spanish and French leagues don't finsh until 30th/31st May so realistically don't expect any movements until mid-June by the time fees and personal terms have been agreed.
You will also find that most clubs don't do business until the last 3-4 weeks before the season kicks off to avoid paying players during the 'down time'. However, if Hughes wants to go to his training camp again I would expect him to get most of targets in before the players come back in early July.