The 23-year-old has been missing for a month, with authorities focusing their efforts on the Carlton Reserve in Florida.
He was last seen just days after Ms Petito was reported missing.
Ms Petito’s body was subsequently found, and a coroner confirmed this week she died by strangulation.
In a TV special aired on Wednesday, John Walsh, the former host of America’s Most Wanted, shared his thoughts on where Mr Laundrie might be.
The presenter reportedly said his current show In Pursuit With John Walsh has received “over a thousand solid tips” with possible sightings.
Most of them were about a theory Mr Laundrie may have headed to Mexico, Mr Walsh was reported as saying.
“Most of them are about my theory of his father driving him to the Mexican border and letting him go through Mexico,” Mr Walsh was reported as saying.
“It’s a great time to be heading south, because [there are] thousands of refugees ... I mean, he could walk across the border naked with his hair on fire, and nobody would notice him.”
According to the NY Post, he added: “I think that’s maybe where he’s hiding — and somebody might be helping him.”
Mr Walsh, who became a victims’ rights advocate after his six-year-old son was kidnapped and murdered in the 1980s, reportedly said there had also been lots of tips about the Appalachian Trail in eastern US.
The Laundrie family attorney said last week he believed Mr Laundrie was alive and hiding out in the Carlton Reserve, despite not having been seen for several weeks.
The search for Mr Laundie has been mainly centred on this 25,000-acre area, which is near his family home in Florida.
Police have said there was a 50 per cent chance of Mr Laundrie – who remains a “person of interest” in Ms Petito’s case – still being alive.