Florida Governor Ron DeSantis and his Texas counterpart Greg Abbott, two future possible Republican presidential contenders, beat back Democratic challengers to win re-election in the US midterms.
The former president told Fox News: "I think he would be making a mistake. I think the base would not like it” and threatened that he would release unflattering information about the 44-year-old.
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Hide AdBoth men have been tipped to announce presidential runs and become likely rivals for the Republican nomination, with Donald Trump scheduled to give an announcement on November 15.
Trump took aim at the rising Republican star who is expected to run for office, branding him as "Ron DeSanctimonious" at a rally over the weekend.
"I don't know if he is running. I think if he runs, he could hurt himself very badly. I really believe he could hurt himself badly. I don't think it would be good for the party."
In Georgia, Democratic Senator Raphael Warnock and Republican challenger Herschel Walker were vying for a seat that could determine control of the Senate, with Georgia set for a run off if no candidate wins 50 per cent of the vote.
CNN have also projected a major upset in the polls, with John Fetterman projected to beat TV personality Dr Oz in Pennsylvania.
Republicans have bet that messaging focused on the economy, gas prices and crime would resonate with voters at a time of soaring inflation and rising violence.