Several publications suggested last week that the president-elect would offer the star a top job in the arts.
In a statement, Stallone said he was "incredibly flattered to have been suggested to be involved with the National Endowment for the Arts (NEA)".
But the star said he would prefer to highlight issues faced by US veterans.
"I believe I could be more effective by bringing national attention to returning military personnel in an effort to find gainful employment, suitable housing and financial assistance these heroes respectfully deserve," the statement said.
Stallone, famed for his role in the Rambo and Rocky films, is also an artist.
He has created hundreds of artworks and last year exhibited at the Modern Art Museum in Nice, France.
In 2013, a collection of his paintings went on display at The Russian Museum in St Petersburg.
At the show's opening the star said, if he had the choice, he would spend his life drawing instead of acting.
"I think I'm a much better painter than an actor," he said.
The Oscar-nominated actor studied art before his film career took off.
In an interview with Variety earlier this year, Stallone said: "I love Donald Trump. He's a great Dickensian character. You know what I mean? There are certain people like Arnold [Schwarzenegger], Babe Ruth, that are bigger than life. But I don't know how that translates to running the world."
Established in 1965, the NEA is an independent federal agency which distributes government grants to arts organisations.
The NEA has come under threat in the past from previous Republican governments, including Ronald Reagan's administration.
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Satnam Singh, 74, was found with serious injuries in a Derby street in July 2015 - opposite the Sikh temple where he volunteered.
Police initially thought he had been hit by a car but last year arrested 30-year-old Sukhraj Atwal for murder.
Mr Atwal denies the charge. His defence said there was a lack of "real evidence" and witnesses.
The prosecution has previously alleged Mr Singh - the defendant's former step-grandfather - was "brutally assaulted" over a long-running family dispute.
The trial at Nottingham Crown Court claimed Mr Atwal repeatedly stamped and jumped on Mr Singh in the early hours of 23 July.
The victim was found with 41 fractures to his ribs, lacerations to his heart, a fractured skull and severe brain damage.
The attack itself was not captured on CCTV but Mr Atwal's car was seen entering and leaving the area shortly before Mr Singh was found.
Defending barrister Shaun Smith, said the case was based on "half-baked theories" and "speculation".
"There is no footage of what happened," he added.
"There are no eye witnesses and when it comes to real evidence there's nothing.
"Nothing to place him at the scene on his footwear or his car, no-one to hear or see it [the attack], or hear cries of distress or see anyone run into a car."
He said although the victim and defendant lived just streets apart "they ignored and blanked one another" and "barely knew" each other.
Mr Atwal chose not to give evidence in court.
The trial continues.
Actor Sylvester Stallone has said he is "flattered" by reports that Donald Trump may offer him an arts post - but would prefer a role helping veterans.
[NEXT_CONCEPT]
The trial of a man accused of murdering a pensioner in the street has heard he "had no motive" to kill him.