Rooney, 28, has been questioned as England head into the World Cup, with his form and ability to perform on the biggest stage coming under the spotlight.
But Hodgson is bemused by the speculation, and insists the Manchester United star remains a "very important member of the squad" as the Three Lions prepare to tackle a tough Group D, where they will face Italy, Uruguay and Costa Rica.
"It is a bit sad that the country is so Wayne Rooney-obsessed," he told reporters.
"I don't think Wayne sets himself up to be anything other than a very important member of the squad, someone who does his best and tries his best at all times.
"Talk about combinations doesn’t interest me. All I want is for Wayne Rooney to play well and Daniel Sturridge to play well.
"We don’t share this obsession with Wayne, we also think that people like Danny Welbeck, Sturridge, Raheem Sterling, Ross Barkley and Adam Lallana are in there to play well and help us score goals, too.
"That's what a squad is about."
Another of Hodgson's strikers, Rickie Lambert, appears close to finalising a move from Southampton to Liverpool and the former Reds boss has congratulated the 32-year-old.
"I congratulate him. And I congratulate Liverpool [for] signing a good player," Hodgson said.
"When he plays you will see a fella running around with all the joy that his heart can muster because he is very happy to be with England and he's very happy that the move to Liverpool has gone through."