Sources spoke on condition of anonymity due to the on-going negotiations.
Details of the initiative are expected to be released Tuesday morning that will lead one of nine state senators opposing the private option to switch their vote.
State senator Jonathan Dismang, R-Searcy, said Monday needed support for the private option had not materialized but that discussions continued despite the federal holiday.
"A big portion of it right now is some individual members have concerns about how different programs have really been run in the past so kind of working through that," Dismang says. "There is a tie in with those programs and the private option and really we're not at a point to fully discuss that at this time."
The Arkansas House is expected to vote on funding for the private option on Tuesday.
The $915 million appropriation includes language preventing state agencies from accepting federal grant money or expending financial resources on outreach and education for the private option or the health insurance exchange.
Dismang added that if changes are made on the Senate side it would not require the House to approve the private option appropriation twice.
Copyright 2016 Nexstar Broadcasting, Inc. All rights reserved. This material may not be published, broadcast, rewritten, or redistributed.