WASHINGTON -- The Supreme Court will wrap its 2017 session on Monday, which could include a decision on President Trump's controversial travel ban.

The Supreme Court usually saves their most important decisions for their final day, and CBS News' Paula Reid says it's very likely they have come to a decision and they make that decision public on Monday. The justices met Thursday for their last scheduled private conference of the session.

The White House has asked the Supreme Court to allow it to go ahead and actually start enforcing this policy and hear arguments about in the fall. The Trump administration believes the Supreme Court is its best hope of having this policy upheld after two lower courts blocked, it saying it's likely unconstitutional.

The Supreme Court will wrap its 2017 session on June 25, 2017. CBS News

It will take five votes from the court to reinstate the ban, but only four votes to set the case for argument. The biggest question mark is Neil Gorsuch, Mr. Trump's nominee who will rule on this high-profile case just three months after joining the bench.

Get Breaking News Delivered to Your Inbox

The case is at the Supreme Court because two federal appellate courts have ruled against the Trump travel policy, which would impose a 90-day pause in travel from citizens of Iran, Libya, Somalia, Sudan, Syria and Yemen.

The 4th U.S. Circuit Court of Appeals in Richmond, Virginia, said the ban was "rooted in religious animus" toward Muslims and pointed to Trump's campaign promise to impose a ban on Muslims entering the country as well as tweets and remarks he has made since becoming president.

The San Francisco-based 9th U.S. Circuit Court of Appeals said the travel policy does not comply with federal immigration law, including a prohibition on nationality-based discrimination. That court also put a hold on separate aspects of the policy that would keep all refugees out of the United States for 120 days and cut by more than half, from 110,000 to 50,000, the cap on refugees in the current government spending year that ends Sept. 30.

Trump's first executive order on travel applied to travelers from the six countries as well as Iraq, and took effect immediately, causing chaos and panic at airports over the last weekend in January as the Homeland Security Department scrambled to figure out who the order covered and how it was to be implemented.

A federal judge blocked it eight days later, an order that was upheld by a 9th circuit panel. Rather than pursue an appeal, the administration said it would revise the policy.

In March, Trump issued a narrower order, but it too has been blocked.

The justices have a range of options. They could immediately allow the administration to stop travel from the six countries and hear arguments on the administration's broader appeal in October. That's the path the administration has urged.

But those who oppose the travel ban say it was only supposed to be temporary, about 90 days, and by the time it actually gets to the court it would have been long past it's actual purpose, Reid says.

Meanwhile, there are rumors swirling that Justice Anthony Kennedy, age 80, could announce his retirement. Kennedy is often the "swing vote" on the court, and if he retires, Mr. Trump could push the court toward a conservative direction for decades to come.

But it's far from certain that any announcement is coming. Sources tell CBS News the White House and the other justices are in the dark about Kennedy's plans.

Retirement announcements do tend to come last day of the term, Reid says, but with Kennedy, you never know what he is going to do.