Chelsea full-back Cesar Azpilicueta has been handed a new five-year deal by the Premier League leaders.
Scottish FA confirms it will apply to FIFA for an exception to help push through John Guidetti's loan move to Celtic.
Diouf has joined Stoke on a four-year contract after leaving Hannover and will be expecting to lead the attack when the new Premier League season gets underway on August 16.
Stoke have also been linked with Stuttgart's Bosnian striker Vedad Ibisevic, a move which would push Crouch, who has only one year remaining on his current deal at the Britannia Stadium, further down the pecking order.
Hughes, however, insists the 33-year-old has a 'big part to play' in his plans for the forthcoming season.
"Peter did very well last year," Hughes told Sky Sports News. "Obviously people picked up on something I said a couple of weeks back about some players arriving so some players will feel that they have to leave.
"Peter isn't one of those I hope because he was exceptional last season, did really well for me. He's a great asset on and off the field so we don't want Peter to leave. He's got a big part to play."
Hughes, who has also signed Phil Bardsley, Steve Sidwell and Dionatan Teixeira this summer, said he will "probably" make further additions to his squad before the close of the transfer window, but, although he did not rule out a move for Ibisevic, the Welshman insists there is no pressure to strengthen his frontline with Diouf already on board.
"We've got a number of irons in the fire, it's fair to say that," Hughes said. "I think the pressure is off in terms of getting people in striking areas. We're really pleased that we've been able to bring in Mame Diouf, we think he's going to really add to what we did last year.
"We're pleased that we've been able to do a good bit of business early on in the window, that's important for us. The lads were in for their first couple of days this week and that's important because they get to know their team-mates very quickly.
"We will benefit from that rather than waiting until the last throws of the window and then trying to introduce players which makes it more difficult in my view.
"We're quite comfortable where we sit but obviously if an opportunity comes to bring in a quality player then we'll pursue it."
A strong second half to last campaign saw Stoke finish ninth in Hughes' first season in charge but the 50-year-old insists the challenge now is to follow that up with another top-half finish.
He added: "We finished really strongly, which we felt we would do.
"It was always going to be difficult for some players initially because there was a lot of change going on. The previous manager had been in place for such a long period of time so I came in with my staff and different ideas, and initially it takes a little bit of time to get used to those.
"But fair play to the guys, they embraced everything and the second half of the season was exceptional to be perfectly honest. We finished where we wanted to be. We set targets and thankfully we hit them.
"Ninth in the Premier League is a huge achievement for us, but I said when I got the job that my aim was to make sure Stoke City were consistently in the top half. We've made a good start but the challenge is to do it again and again."