Palmer, 22, enjoyed a stand-out campaign for Chelsea last season, scoring 22 Premier League goals and providing 11 assists.
Manager Gareth Southgate has used Palmer sparingly so far, but he again impressed when he was sent on for the second half of the last-16 match against Slovakia, when England came from behind to win after extra time.
London-born Duah is a Chelsea fan and admits he has been left perplexed as to why Palmer has not seen more game time ahead of the quarter-final with Switzerland in Dusseldorf on Saturday.
“He (Palmer) did a very, very good season last year,” Duah told a press conference.
“I am also thinking: ‘why is he not playing?’ because his stats were perfect in my opinion, so let’s see if he starts on the weekend.”
Ludogorets forward Duah added: “Of course, I follow English football. I would say I am a big Chelsea fan, my idol is Didier Drogba.”
Duah — who moved to Switzerland with his parents at the age of two — scored in the 3-1 win over Hungary in the group stages, where they also came within minutes of beating Germany before the hosts scored a stoppage-time equaliser.
After going on to knock Italy out in the last 16, Duah feels England will not underestimate Murat Yakin’s side.
“I think they will have watched the game against Italy and we were pretty good, so I don’t think they will do that,” he said.
“We are expecting to face a very good team, with big names, so we want to do our best and show what we can do.”