By Caroline Kelly, CNN

(CNN) -- President Donald Trump said Friday that a former president had commended him for his commitment to securing funds to build a wall along the nation's southern border.

However, none of the four living former presidents have said they told Trump they wished they had built the wall.

In a news conference Friday, Trump suggested that at least one prior commander in chief had agreed with his desire to build a wall.

"This should have been done by all of the presidents that preceded me," Trump said. "And they all know it. Some of them have told me that we should have done it."

But his predecessors have denied such a conversation.

Jimmy Carter, the oldest living former president, said Monday that it wasn't him.

"I have not discussed the border wall with President Trump, and do not support him on the issue," Carter said in a statement tweeted by The Carter Center on Monday afternoon.

Freddy Ford, a spokesman for former President George W. Bush, told CNN that "they haven't discussed this."

Former President Bill Clinton spokesman Angel Urena said Clinton "never said that," adding that "they've not talked since inauguration."

A spokesman for Trump's immediate predecessor, Barack Obama, did not respond directly to a CNN request for comment, instead passing along comments Obama made as president in which he said a wall isn't necessary.

"A nation ringed by walls would only imprison itself," Obama told the assembled representatives of the UN's member states in September 2016.

In a commencement address at Rutgers University in May 2016, Obama blasted the idea and said a wall was antithetical to America's history of attracting and growing from "strivers."

"Suggesting that we can build an endless wall along our borders, and blame our challenges on immigrants -- that doesn't just run counter to our history as the world's melting pot; it contradicts the evidence that our growth and our innovation and our dynamism has always been spurred by our ability to attract strivers from every corner of the globe," he said to a cheering crowd.

Obama's representatives didn't respond to CNN last week when asked if he was the former president who had spoken with Trump and praised the wall. CNN reached out to Obama's representatives again Monday.