President Donald Trump speaks about the government shutdown on January 25, 2019, from the Rose Garden of the White House in Washington, DC. -

President Donald Trump told a conservative media outlet he believes he is "confined" to a list of 25 potential Supreme Court nominees that his administration released in 2017 for his next pick for the top court.

The list, which was released during the 2016 presidential campaign and updated in Trump's first year in office, was compiled with the assistance of people tied to conservative groups including the Federalist Society and the Heritage Foundation.

Speculation about Trump's next potential nominee has taken on newfound significance because of concerns about liberal Justice Ruth Bader Ginsburg's health. Ginsburg underwent cancer surgery late last year, forcing the 85-year-old to miss her first oral arguments in her 25 years on the bench as she recovered.

"I have very much confined myself to that list as you know … that list has great people on it … and I'd say it's highly likely I would say," Trump told The Daily Caller in an interview for an article published late Wednesday.

Trump's first nominees to the court, who both came from the short list, have strong ties to the Federalist Society. Justice Neil Gorsuch spoke at the group's annual conference in 2017. In his Senate confirmation questionnaire, Justice Brett Kavanaugh said his ties to the group lasted from 1988 to the present. He attended the group's conference last year.

Trump told the outlet he would not commit to nominating Judge Amy Coney Barrett, a favorite among social conservatives and particularly among opponents of abortion.

Trump was criticized by some conservatives for his selection of Kavanaugh instead of Barrett last year, and that criticism has grown since Kavanaugh was confirmed to the bench.

"Anybody on that list would be a choice," Trump said in the interview. The president, who wished Ginsburg a speedy recovery on Twitter after her surgery, said he hoped she was healthy.

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His administration has reportedly begun preparations in case she departs from the bench.

"I hope that she's healthy … I hope she's happy … I hope she lives for a long time," he told The Daily Caller.

The White House did not respond to a request for comment about Trump's interview.

The ideological balance on the Supreme Court will likely play a major part in the 2020 presidential campaign. Social conservatives who had qualms about Trump in 2016 backed him largely for his dedication to appointing conservative judges to federal courts. The Supreme Court now has five conservative justices and four liberals.

No 2020 Democratic contender has said whether they will release short lists during the campaign as Trump did. Only one candidate, former Maryland Rep. John Delaney, responded to CNBC's inquiry on Wednesday about the matter. His press secretary Michael Hopkins said they "haven't ruled anything out."