The former Manchester City and Blackburn boss took over from Tony Pulis in the summer.
“He is wonderful, a real manager who takes care of everything,” Begovic told Dnevni Avaz.
“He was a great player, his standards are extremely high. Often in training he can still show things to the players, he is still in great shape and form.”
He added: “Although the current results are not the best, I think Stoke did a great job of bringing Hughes and we are playing much better football.”
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Since Guus Hiddink arrived at the helm, Chelsea have improved considerably after a tricky start to the campaign.
Newcastle United are staring down the barrel of relegation to the Championship for the second time in the past eight years.