To be sure, Kennedy has given no public sign that he will retire this year and give President Trump his second high court pick in the first months of his administration. Kennedy’s departure would allow conservatives to take firm control of the court.

But Kennedy turns 81 next month and has been on the court for nearly 30 years. Several of his former law clerks have said they think he is contemplating stepping down in the next year or so. Kennedy and his clerks were gathering over the weekend for a reunion that was pushed up a year and helped spark talk he might be leaving the court.

‘‘Soon we’ll know if rumors of Kennedy’s retirement are accurate,’’ one former Kennedy clerk, George Washington University law professor Orin Kerr, said on Twitter on Friday.

When the justices take the bench Monday, they are expected to decide the case of Trinity Lutheran Church of Columbia, Mo., which was excluded from a state grant program to pay for soft surfaces on playgrounds run by not-for-profit groups.

The case is being closely watched by advocates of school vouchers, who hope the court will make it easier to use state money to pay for private, religious schooling in states that now prohibit it.

Missouri has since changed its policy under Republican Governor Eric Greitens so that churches may now apply for the money.

Also expected in the next few days, though there’s no deadline by which the court must decide, is a ruling on whether to allow the administration to immediately enforce a 90-day ban on visitors from six mostly Muslim countries.

Justice Neil Gorsuch, Trump’s first Supreme Court nominee, could play a pivotal role in both the travel ban and church playground cases.

In all, six cases that were argued between November and April remain undecided. Three of those, all involving immigrants or foreigners, were heard by an eight-justice court, before Gorsuch joined the bench in April.

If the eight justices are evenly divided, those cases could be argued a second time in the fall, with Gorsuch available to provide the tie-breaking vote.

In his short time on the court, Gorsuch has already paired up four times with Justice Clarence Thomas — the court’s most conservative member — in separate opinions that dissent from or take issue with the court’s majority rulings.

While the sample size is small, the results show Gorsuch’s commitment to follow the strict text of the law and a willingness to join Thomas in pushing the envelope further than the court’s other conservatives.

Gorsuch was picked by Trump to be a reliable conservative in the mold of the late Antonin Scalia. But the question after his confirmation hearings was how far to the right he would be.

The early trend of Gorsuch and Thomas acting together has pleased those who hoped Gorsuch would continue Scalia’s legacy and be another intellectual beacon for conservatives.

The latest instance came Friday when Gorsuch issued his first written dissent in a minor case about a federal employee challenging his dismissal from the US Census Bureau. The dispute was over where Anthony Perry could appeal a case that alleges violations of both federal civil service rules and laws prohibiting discrimination.

The court sided with Perry, ruling 7 to 2 that he could file his lawsuit in a federal district court instead of first waiting for a federal appeals court to consider part of his case. In dissent, Gorsuch faulted the majority for failing to apply the law as written.

‘‘Anthony Perry asks us to tweak a congressional statute — just a little — so that it might (he says) work a bit more efficiently,’’ Gorsuch said, joined by Thomas. ‘‘No doubt his invitation is well meaning. But it’s one we should decline all the same.’’

Later, he added: ‘‘If a statute needs repair, there’s a constitutionally prescribed way to do it,’’ Gorsuch said. ‘‘It’s called legislation.’’

A day earlier, Gorsuch wrote a separate opinion when the Supreme Court unanimously limited the government’s ability to strip US citizenship from immigrants who lie during the naturalization process.

Joined by Thomas, Gorsuch said the majority ruling was correct, but he argued that following ‘‘the plain text and structure of the statute’’ was enough.