Arnautovic's form has been key to the recent upturn in Stoke's form.
The Potters endured their worst start to a season since their promotion seven years ago, but have now lost just one of their last 10 matches.
Arnautovic has scored three goals - including the winner against Chelsea - and laid on two assists in his 11 appearances so far this term.
The Austrian winger, who joined from Werder Bremen two-and-a-half years ago, has 18 months to run on his contract and Hughes hopes the player will agree an extension soon.
"I'm thinking about it (Arnautovic's contract) and I'm sure Marko is," the Stoke manager said
"We want him to stay."
Arnautovic arrived in England with a bad-boy reputation.
While at Inter Milan then-boss Jose Mourinho described Arnautovic as "a fantastic person", but added that "he has the ÂÂattitude of a child".
And Bremen suspended him after he was pulled over in his sports car by police for speeding in the early hours of the morning before a match.
Hughes has nothing but kind words to say about the 26-year-old, however.
"I think his manner and his personality takes people aback initially, but once you get to know him he is very gregarious, he likes people and he likes being around them," the Welshman said.
"He likes a little bit of attention, but that's fine
All the guys love him.
"He's not only a great character, but he's doing well for the team and credit to him.
"The two years he has had here have been good, but there is the potential to have a better year this year if he keeps continuing to play as well as he is."
Another player Hughes does not want to lose is Phil Bardsley.
The right-back is unlikely to feature against his old club Sunderland on Saturday as he has lost his place to Glen Johnson following his arrival from Liverpool.
The former Manchester United defender has played just one league match so far this season and was sent off on his last appearance in the Capital One Cup against Chelsea.
Hughes has been impressed by Bardsley's attitude in training, however, and is not looking to let the 30-year-old leave the Britannia Stadium in January.
"I am not really looking to get Phil out," the Stoke manager said.
"It's important that we have that defensive cover, so a loan deal for Phil is not something I am really looking to do."
Source : PA
Source: PA