I want you to step back and really consider the reporting on this by taking into context the kind of reporting of the behind-the-scene Trump Administration actions that came out of the media. And given that, I have no idea how you can possibly take this interpretation at face-value.
For the last 4 years, there has been an egregious claim after another, each more bonkers than the next, unverified, stemming from some 'anonymous sources' against Trump that has time and time again proven to be without merit. Every.single.week.
Just recently, a news cycle was devoted to the claim that Trump will barricade himself in the office if Biden wins. Just prior to the election, multiple news cycles were devoted to reporting on Trump destroying postal boxes to prevent mail-in voting. A little before that, Trump was accused of ignoring Russian bounties on American soldiers (another meritless claim that was disavowed by the the Taliban, Russian, American Intelligence and Army with no evidence presented by NYTimes). Again, this occurred every single week for the last 4 years.
And you don't even have an ounce of skepticism of reporting that Trump in a private conversation asked governors to break the law, given how this kind of stuff has been reported, time and time again?
The gaslighting of the last 4 years has been insane and the media is simply incapable of objective straight reporting on Trump. I know how that sounds, but that's what it is.
Whether he should do it is a different question.
The theory here is that the US Constitution, because of wording in Article II ("Each State shall appoint, in such Manner as the Legislature thereof may direct, a Number of Electors [...]") that if interpreted hyperspecifically[1] implies that the legislature alone, and not Governor or state law, has the power to appoint electors. That has never been tested in practice.
But regardless, it would still be a state crime to do it. So no, he doesn't have the right.
[1] Obviously the reasonable interpretation of this line is "States decide for themselves how to choose electors", not something that makes assumptions about the structure of state government.
Whether people have the right to request governors to perform illegitimate actions... that probably depends on your definition of "right", and I don't care very much about having that debate.
He does not have the right to ask state governors to ignore the election results and appoint electors who will vote for Trump. That is far beyond the legitimate exercise of Trump's rights.