Reports in the Italian media suggested he will complete a £5.3 million permanent transfer.
Parker, 36, helped his last club Fulham, for whom he played for four years, to reach the Championship playoffs.
Klinsmann, 52, has been out of coaching since November, when he was sacked by the U.S.
Hughes, 22, has put pen to paper on a five-year contract at Vicarage Road and joins for an undisclosed fee.
Former England midfielder Stewart Downing has been told he can leave Middlesbrough on a free transfer this summer, according to multiple reports.