The U.S. Supreme Court has previously rejected Pennsylvania Republicans' requests to block the extension, but four justices last month did signal openness to potentially take up the case on the merits after Election Day.
There is no any timeline for a decision on that.
By asking that he added as a party, Trump seems to be attempting to boost the chances the justices will take it up.
"Given last night's results, the vote in Pennsylvania may well determine the next President of the United States. And this Court, not the Pennsylvania Supreme Court, should have the final say on the relevant and dispositive legal questions," the president's lawyers wrote in the filing.
It remains unclear if the U.S. Supreme Court will take up the matter. It's also unclear whether the justices' involvement would have any impact on the outcome in Pennsylvania.
The universe of votes arriving through Friday is not yet known, nor is the ultimate margin of votes between Biden and Trump in Pennsylvania and whether those late-arriving ballots would sway the results one way or the other.
Trump vowed in a speech in the early hours of Wednesday morning to take his grievances to the Supreme Court, a move Democrats say they expected given Trump has signaled the move for weeks.
Anticipating a legal battle, Pennsylvania officials are "securely segregating" mail ballots that arrive after Nov. 3 through 5 p.m. Friday in the event that they need to be invalidated.
ABC News' John Santucci and Benjamin Siegel contributed to this report.