Trump Looking to Take on Biden in 2020 Election President Donald Trump says he "dreams" about running against former Vice President Joe Biden in the 2020 election. Donald Trump, via interview with CBS Trump went on to point out that the former Delaware senator ran for president twice unsuccessfully. Although Biden has copped to considering a run, he has yet to commit to anything. Joe Biden on 2020 Presidential run In a Harvard poll last month, Biden led the pack of potential party nominees, with 32 percent of Democrats polled supporting him.