But according to the Hollywood actor, who served two terms as the Republican Governor of California, this animosity comes from a place of love.
Floating a new theory about the president, Schwarzenegger, who revealed he was stepping down from hosting The Apprentice last week, went so far as to suggest Mr Trump was “in love” with him.
President Trump, who hosted The Apprentice for 14 years before Schwarzenegger took over, has often attacked his successor in Twitter tirades.
Appearing on US SiriusXM radio show, Schwarzenegger was pressed about why Mr Trump has a “fixation” with him.
Schwarzenegger simply replied: “I think he’s in love with me.”
“You’ve had a long relationship with him,” the host replied, prompting Schwarzenegger to simply say: “Oh, yes.”
The actor was asked to elaborate on where this infatuation came from but declined.
One theory which has been floated as a potential reason for Mr Trump's apparent hatred for Schwarzenegger is the fact he apparently wanted Ivanka Trump, his third child who is said to be his “favourite”, to take over from him on the show.
Alongside her brothers Eric and Donald Jr, Ms Trump was a mentor and judge on the show, and Mr Trump reportedly thought she would be the perfect candidate to host.
The billionaire property developer, who continued to be an executive producer for the show after his election, launched the reality TV series in 2004 and continues to hold it dear to his heart.
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The highly public spat started after Mr Trump mocked Schwarzenegger in January after the premiere of the new season. “Wow, the ratings are in and Arnold Schwarzenegger got ‘swamped’ (or destroyed) by comparison to the ratings machine, DJT,” he wrote on Twitter. “So much for being a movie star.”
While Schwarzenegger’s debut episode attracted 4.93 million viewers, Mr Trump’s debut episode in 2008 was watched by 11.08 million and his last amassed 6.1 million.
After Schwarzenegger announced he was quitting the show, citing Mr Trump’s “baggage”, the President snapped back and claimed the actor was "fired by his bad (pathetic) ratings”.
Since revealing he was quitting, Schwarzenegger has said the programme was somewhat tainted by Mr Trump’s presidency.
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