The West Ham forward has scored five goals in 10 league games this season, even though Manuel Pellegrini's side have won just one of their past five top-flight fixtures.
"It's not that he really wants to leave, but we believe this is the moment in his career when he has to take a step forward and try to win a few trophies, maybe even the Champions League," he told gianlucadimarzio.com.
"There are a lot of Premier League clubs tracking him. Chelsea and Everton, for example, but not only them."
"Why not?" Daniel said, when asked about a return to Italy. "He could prove that Inter weren't wrong to take a gamble. He was only 19 when he joined Inter and left many good friends behind there, along with fond memories of Milan."
Speaking earlier, the Austria international told Kurier newspaper: "I'm 29, so at my best age. It's clear that I want to compete with the very best. But I fully trust my brother in such matters."
His brother added that Arnautovic was ready for "the next step" in his career, even though he is happy with life at London Stadium.
"Marko feels extremely comfortable at West Ham. You can see that every week," he said. "But you also get the feeling this cannot be the end. He's ready for the next step.
"Someone like him should not be fighting against relegation but playing for the best seats and for the international places."