The ten-page document has been sent to the prestigious universities Vanderbilt University, University of Pennsylvania, Dartmouth College, University of Southern California, Massachusetts Institute of Technology (MIT), University of Texas, University of Arizona, Brown University and University of Virginia.
They are urged to adopt the White House's vision for the direction in which the US universities should be headed.
If the universities accept, they will be given priority for federal grants.
It is about, among other things, how admissions should be handled, freedom of speech and discipline among students at the institutions. But also that the universities should adopt the Trump administration's definition of gender – since previously, trans people's opportunity to participate in sports in the US under Trump's rule – and apply it to women's sports.
Several of the universities have not wanted to comment, while representatives of the University of Texas say they are "honored" to be one of those asked.
Donald Trump has been in several notable conflicts with prestigious universities such as Harvard, Columbia and UCLA. It has, among other things, been about admissions and political orientation at the institutions.