The President doesn’t get to decide on that any more than a regular citizen. The Fourteenth Amendment of the Constitution states quite clearly that “All persons born or naturalized in the United States, and subject to the jurisdiction thereof, are citizens of the United States and of the State wherein they reside.”
If Congress and the States want to amend the Constitution, they can do so by following the procedures laid out in Article V, which requires a 2/3 majority of both houses of Congress OR 2/3 of state legislatures to propose the amendment, and then 3/4 approval of state legislatures to ratify it. The President has zero involvement in the process:
Once approved by Congress, the joint resolution proposing a constitutional amendment does not require presidential approval before it goes out to the states. While Article I Section 7 provides that all federal legislation must, before becoming Law, be presented to the president for his or her signature or veto, Article V provides no such requirement for constitutional amendments approved by Congress, or by a federal convention. Thus the president has no official function in the process. In Hollingsworth v. Virginia (1798), the Supreme Court affirmed that it is not necessary to place constitutional amendments before the president for approval or veto.
Problem is, conservatives have been trying to have a constitutional convention for a while. It’s a goal of theirs to get enough state legislatures to do it. Should that happen, we’re in for a really bad time.
Theoretically you can amend the constitution at will if you control congress, the presidency, and one state legislature. You just carve up (for example) Texas to create another 150 states out of a rural area with each occupied by loyal party members. Then you admit them (only need a simple majority) and use them to push through any amendments you want. This would almost certainly trigger a civil war, but as far as I know it is legal.
