Baggies manager backs Italian tactician to effectively handle the saga, and has also offered his support to under-fire Sunderland chief Steve Bruce
The Argentina international refused to come off the bench during his side's 2-0 defeat to Bayern Munich on Tuesday and has since been suspended but, according to the Baggies boss, if anyone can deal with the restless star, it's the Italian.
"I'm sure at all levels of football at all times, these sort of situations have come up and if anyone if capable of dealing with it, it will be Roberto," Hodgson told reporters.
"He's worked in Italy and he knows the Italian mentality and this type of problem, if we call it that, has reared its head many a time in Italy.
"I'm sure he knows how to deal with it."
Hodgson boss believes professionals should do as a professional does and ultimately is thankful he's not had similar issues yet at Albion.
"It is not the best time to say too much but you bring players into your squad to play for you," the well-travelled Englishman said.
"The manager has to make decisions about who does and doesn't play, and the club is entitled to expect anyone not chosen by the manager, if called upon, is ready to play when and if asked.
"The situation is black and white. There is not much shade of grey.
"But it is a Man City problem."
"I'm just happy to be working with modern day players personally and happy those problems haven't reared their head for me here."
Hodgson also showed support for fellow Englishman Steve Bruce to overcome his poor start to the Premier League campaign at Sunderland.
The Black Cats are ahead of the Baggies in the table by a single point, but Bruce has been increasingly under the kosh after an active summer transfer window yet to yield positive results.
The West Brom boss is sure of Bruce's quality as a manager, but probably hopes he doesn't come good until after the two square off on Saturday at the Stadium of Light.
"Steve is a good manager and has done a remarkable job wherever he has been.
"I think he and the club are more than strong enough to withstand whispers and rumours.
"It would surprise me if a club like Sunderland had any knee-jerk reaction.
"It is still early days in the season and Steve is in the throes of putting together a new team because, in the transfer market, he was very active this year.
"We all know it takes time to gel together."
Hodgson elaborated on the phenomenon of knee-jerk reactions to only a few poor results, reminding that circumspection is required in the face of week-to-week pathos.
"I think the itchy-finger syndrome is with us all the time in football.
"We are used to that but only hope the people in football who make decisions make good ones."
The former Liverpool manager is also confident that Peter Odemwingie, the Baggies' leading scorer last season with 15 goals, can find his touch in front of goal once again
He said: "It is early days. He is playing very well in training.
"Like everything else, if a forward scores a goal from a goal chance, then he is said to be playing fantastically well.
"If he misses the goal chance, he is said to be having a bad time.
"That is what forwards have to live with. But we are quite happy with Peter.
"He looks very lively, very fit and we hope we can keep him fit for the next 30-odd games."