The day for elections is established in the Constitution, so any such change requires new legislation. The 20th Amendment to the Constitution also specifically states that Presidential terms conclude on the following January 20th, Inauguration Day. No legislation is likely to be passed that would allow for any change.

The next person in order of succession is the speaker of the House. However, if there were no election, that seat would too be vacant, as the House has two-year terms that conclude on January 3 following the election. The next individual in line is president pro tempore of the Senate, who is the senior Senator of the majority party and presides over the Senate in the Vice President’s absence. The Senator who holds the title – Chuck Grassley of Iowa – is also up for reelection in 2020, and so his seat would similarly be vacant if no election were held. Because of the number of Senate seats up for re-election, if no election was held, Democrats would gain the majority in the chamber, and because the process of selecting the president pro tempore is informal, could choose any among them.

Trump claimed he lost the 2016 popular vote because of widespread fraud, though the commission he established to investigate it found none. Since then he has disparaged mail-in and other measures for easier voting, though he and his family vote by mail themselves, and has yet to confirm if he would accept 2020 election results.

At the same time that Trump made the suggestion to postpone elections amid the COVID-19 pandemic, his administration pushed for a full re-opening of schools across the United States.

NPR – Trump Floats Delaying The Election. It Would Require A Change In Law
Constitution Daily – Does the Constitution allow for a delayed presidential election?
Politico – Postpone the Election? That Could Mean President Biden