The Republican presidential nominee is due to campaign on Wednesday evening in Jackson, Mississippi, and the former UKIP leader is also said to be in the southern US state.
Trump campaign spokesperson Hope Hicks told Sky News she would "highly doubt" such a joint appearance.
She added that she knows nothing about it and "they don't know each other".
Mr Trump caused a stir last week with a cryptic tweet in which he said: "They will soon be calling me MR BREXIT!"
The real estate businessman supported June's UK vote to leave the European Union and described it as "the people taking the country back".
Many Trump supporters have voiced nationalist, anti-globalisation, anti-establishment views, which have been echoed among many who voted for Brexit.
During a visit to his Trump Turnberry golf resort in Ayrshire, Scotland, in the aftermath of the referendum, Mr Trump said the UK's vote to leave the EU was a "great thing".
"People are angry all over the world," he said.
"They're angry over borders, they're angry over people coming into the country and taking over and nobody even knows who they are."
