"But here's the problem, if I did it joking, totally joking, having fun, the fake news media will say 'he believes he should be on Mount Rushmore.' So I won't say it. Okay? I won't say it."
Despite the fact he said he won't say that he should be on Mount Rushmore, people on social media quickly loaded up Photoshop and imagined what this future could look like.
This comes after Donald Trump hailed the prospect of an exciting new trade deal with Britain, following outrage over the possible import of chlorinated chicken.
The International Trade Secretary wants to allow the import of poultry after Brexit but is being opposed by Michael Gove, the Environment Secretary, who has insisted food standards must not be downgraded.
Following the controversy, Mr Trump hailed the talks between Dr Fox and US Trade Representative Robert Lighthizer yesterday.
Posting on the official presidential Twitter account, Mr Trump said: "Our special relationship w/ UK is going to be even better. @USTradeRep & UK's @LiamFox met today to begin new chapter for stronger trade!"