The Friends in Low Places hitmaker is said to be considering the big gig, but has yet to sign on for the January (17) event.
"Garth has performed for the five living presidents...," his publicist Nancy Seltzer told Reuters. "While rumour has it that he has been asked to perform for president-elect Trump, he has not been able to commit yet."
The singer has already insisted he wouldn't be opposed to playing for the controversial Republican.
"It's always about serving," he recently told TMZ.com. "It's what you do."
The news emerges amid reports suggesting Trump's inauguration organisers are struggling to secure big names for the bash, which will take place in Washington, D.C. on 20 January (17).
Motley Crue rocker Vince Neil claimed he had initially been asked to play the show last month (Nov16), but was then "uninvited" to the event hours after going public with the alleged booking.
Elton John was then forced to deny rumours he would be gracing the inauguration stage after a key advisor to Trump made the surprise announcement the Brit would be a big part of the gala in a BBC interview.
"This is incorrect," the Rocket Man's representative wrote in a statement emailed to Pitchfork.com. "Elton will not be performing at Trump's inauguration."
The set would have been a big surprise as the singer has previously campaigned for Trump's rival, Hillary Clinton.
Rocker Ted Nugent is also expected to be part of the inauguration - he was campaigning with Trump the weekend before the property tycoon's shock election victory.