The move would make the confederation of nine universities and six health institutions the first to charge for courses delivered through the edX platform.
Meanwhile, universities that "have rushed to offer" free online content have been called "irresponsible" by The Open University's vice-chancellor.
The UT system, which includes the University of Texas at Austin, announced on 15 October that it will offer at least four courses through edX during the next year.
It plans "to eventually offer courses for credit", a spokeswoman for the system told the BBC. "There will be a tuition charge for credit-earning courses, but the amount hasn't been determined."
Universities that have joined free online platforms have been grappling with how to make the system financially viable, and UT is the first to explicitly propose charging students if they want to earn degree credits.
Martin Bean, vice-chancellor of The Open University, told Exporting Excellence: Capitalising on the Global Value of UK Education, a conference held in London on 17 October, that the "rule book" was being torn up by online learning.
The rise of Moocs on providers such as edX had created a "Napster moment for higher education", he said, referring to the growth in free music file-sharing, pioneered by the original incarnation of the Napster website, that has upended the music industry's business model.
He cited major businesses such as the Blockbuster video rental chain that had been driven to bankruptcy after being undercut and circumvented by internet offerings.
Asked whether he thought universities should give away their content for free online, Professor Bean said: "I think there's no doubt that this Mooc frenzy is irresponsible."
He warned that the Mooc model was just "one chapter" in how higher education would be transformed by the internet, so it was "irresponsible" to rush towards it.