The source described the meeting as "positive."
While the House has already passed a bill that would seek to make limited reforms to improve the nation's prison system, the legislation has stalled at the feet of Grassley, the powerful Republican chair of the Judiciary Committee.
Grassley, a longtime advocate for criminal justice reform in Congress, has taken a principled stance in refusing to advance legislation that doesn't include broader sentencing guidelines.
The Senate is now expected to move forward with a modified version of the House bill that will reduce the current mandatory life sentence for certain drug offenses from a life sentence to 25 years, prohibit the doubling of mandatory sentences for certain gun and drug offenses, broaden judicial discretion, and make retroactive the 2010 Fair Sentencing Act that narrowed the discrepancy in sentencing guidelines for crack versus powdered cocaine.
Grassley emerged "encouraged" that the president is supportive of a broader criminal justice reform and expressed optimism that a legislative victory is within reach.
"Progress on this issue has been stalled for too long. I think it's clear now that the President is engaged on this issue and is supportive of a reasonable compromise," Grassley said in a statement to ABC News. "With his leadership I think we can get a bipartisan deal done -- one that's tough on crime, but fair and that gives prisoners trying to improve their lives a second bite at the apple."
Separately, in a meeting with inner-city pastors last week, a source with knowledge of the meeting said the president "essentially came out in support of broad-based reforms to the criminal justice system."
Meanwhile, a White House official pushed back on that characterization, saying the president only expressed his willingness to consider broader reforms if it can be demonstrated that such a package would have success in Congress.
The president has yet to make any public pronunciations of support for sentencing reform. At a meeting on prison reform at his Bedminster club on Thursday, President Trump talked about his administration's support for the legislation currently making its way through Congress but did not volunteer an opinion regarding the modifications that the Senate is weighing to the bill.
The president expressed his pleasure at the "tremendous political support" his administration has found on the issue, saying it's something that surprised him when his administration initially took on the issue a year ago. "Pepole that I’d least suspect are behind it are 100 percent behind it," Trump remarked.
A handful of governors and state attorneys general attended the meeting, along with the president's son-in-law and adviser Jared Kushner, who the president praised for leading on the issue of criminal justice reform within the administration, nothing that the issue is close to his son-in-law's heart.
Kushner's father, Charles Kushner, pleaded guilty in 2005 to 18 counts of tax evasion, witness tampering and making illegal campaign donations. He served 14 months of a 24-month sentence in federal prison and the remainder of his term at a halfway house in New Jersey.
Kushner traveled frequently to Montgomery, Alabama, on weekends to visit his father behind bars.
While Kushner has long supported broad reforms to the criminal justice system, the administration has only come out in public support of narrow prison reforms up until this point, in large part due to the objections of Attorney General Jeff Sessions to sentencing reforms.
A Department of Justice spokesperson did not respond to a request for comment on the expected additions of sentencing reform guidelines to the Senate version of the House bill.
A senior administration official pointed to a letter Attorney General Jeff Sessions sent to Sen. Grassley in February laying out the administration's opposition of sentencing reforms and said that letter continues to be the official policy position of the administration.