Pompeo, a Republican former member of the House of Representatives, has said he has no plans to run for the seat but many Republicans believe he ultimately will do so. The deadline for filing as a candidate for the Republican nomination is not until next June.
In an interview on Fox News Channel's "Fox & Friends," Trump said Pompeo would win easily if he were to run.
"He loves the people of Kansas. If he thought there was a chance of losing that seat (having a Democrat win a seat that is currently held by a Republican), I think he would do that, and he would win in a landslide because they love him in Kansas," Trump said.
Senate Majority Leader Mitch McConnell and other Republicans believe that Pompeo, if he runs, could keep the Senate seat in Kansas now held by fellow Republican Pat Roberts, who has decided not to run for a fifth term, in Republican hands.
They do not have the same confidence in Kris Kobach, a former Kansas secretary of state who has said he is running. Kobach, a conservative hawk on immigration, lost the state's governor's race last year.
Trump named Pompeo as secretary of state in 2018 after firing Rex Tillerson. Prior to that, Pompeo served as Trump's CIA director.
A key witness in the Democratic-led House of Representatives impeachment inquiry against Trump testified on Wednesday that Pompeo was among the senior U.S. officials "in the loop" in the Trump administration's drive to get Ukraine to carry out investigations that could benefit Trump politically.
U.S. Ambassador to the European Union Gordon Sondland also provided correspondence that showed Pompeo's engagement in the matter.
Senator Bob Menendez, the top Democrat on the Senate Foreign Relations Committee, and other Democratic members of the panel asked Pompeo in a letter on Friday to recuse himself from Ukraine-related matters.
"Given your direct involvement in the scandal, you have a profound conflict of interest and you must recuse yourself," they wrote.