The speaker's comments come as the Republican Party tries to unify following a divisive primary fight and fears among conservatives that Trump doesn't embrace their values.
On Thursday, Trump visited Capitol Hill, where he met with Ryan, Republican congressional leaders and Republican National Committee Chairman Reince Priebus in what was hailed as an important step toward piecing the party back together.
Ryan had sent shockwaves through the political establishment earlier this month when he told CNN's Jake Tapper that he was "just not ready"
to endorse Trump.
At the time, Trump said he wasn't ready to "support Speaker Ryan's agenda," though in a joint statement following Thursday's meetings, the two men said they had taken "a very positive step toward unification."
"Our teams are meeting next week to go over the deeper meaning of the policies that we have been talking about that come from the principles we universally share as Republicans," Ryan told reporters late Saturday afternoon at the Wisconsin GOP convention in Green Bay.
He added, "It is no secret that Donald Trump and I have had some disagreements. It's no secret that we've, from time to time, clashed on an issue or two. That happens with people. That happens with Republicans."
Ryan continued, "The question is can we put together a process that really, actually gets our party unified so that we're at full strength in the fall, and based upon the meetings that we had on Thursday, I'm encouraged with the beginning of this process."
Ryan did not provide further details about next week's meeting, including when it would take place, who would be there and what would be discussed.
A message left with the Trump campaign was not immediately returned Saturday afternoon.
At the news conference in Green Bay, the speaker -- who also did not provide a timeline on when he might endorse his party's new standard-bearer -- praised Trump's achievement in securing the Republican nomination.
"Donald Trump should be given a ton of credit for advancing and widening the playing field," Ryan said. "He is bringing new voters to the Republican Party by the millions and that's very impressive. What we want to make sure going forward is that we're doing nothing but adding voters to the Republican Party column, and not doing anything that subtracts voters going forward."
Ryan reiterated his belief that party unification would take time, especially following what he said was "one of the most divisive primaries of the modern era."
The statement echoed Trump's own remarks on the unification process following Thursday's meetings.
"I don't mind going through a little bit of a slow process," Trump told Fox News' Sean Hannity that night. "We're getting there."