Previous manager Roy Hodgson masterminded an incredible transformation of the west London club, taking them from relegation candidates to Europa League finalists during his two-and-a-half-year spell at the club.
The former Wales, Manchester City and Blackburn manager met the squad before they lost 1-0 to Portsmouth in their penultimate pre-season friendly on Saturday.
Greening, who signed a two-year contract this summer following a successful loan from West Brom, was impressed by the meeting with Hughes, and hopes the former Manchester United striker will be able to take the club on after Hodgson's successful reign.
"We met the gaffer about an hour and a half before the game, he said hello to us all," Greening told his club's official website. "The boys are really looking forward to a new start. We knew that he was coming to watch the game but we didn't expect to meet him before the game - so it was nice that he popped in.
"Mark Hughes was a great player and is a great manager so everyone will be looking up to him. (Fulham midfielder) Simon Davies worked with him at Wales and he told us what a good manager he is and how he enjoyed his training sessions. It's a fresh start."