Senate Republicans mostly don't know what's in the healthcare bill expected to be out this week, and some admitted that they don't know who is writing it.

Senate Majority Leader Mitch McConnell told reporters he hopes to release a discussion draft of a healthcare reform bill by Thursday morning. But who is behind putting words on the paper is a subject of some confusion among members of the Republican Senate caucus.

Some Republicans say McConnell's office is behind it, while others believe it is a combination of a few Senate committees. And some just refused to hazard a guess.

When asked if he knows who is writing the bill, Sen. Rand Paul, R-Ky., responded "not exactly."

Sen. Susan Collins, R-Maine, said she didn't know either.

"I assume Sen. McConnell and his staff are, with input from his working group, but I really don't know," she said.

But it remains unclear how much input that working group has on actually drafting the bill.

After the House passed the American Health Care Act last month, McConnell convened a working group of about 14 senators. The idea of the working group was to hash out differences over healthcare and some thought to actually write the bill.

But some senators are complaining it hasn't worked out that way.

"It has become increasingly apparent in the last few days that even though we thought we were going to be in charge of writing a bill within this working group, it's not being written by us," said Sen. Mike Lee, R-Utah, in a Facebook video Monday. Lee has been a member of the group.

"It's apparently being written by a handful of staffers who are members of the Republican leadership in the Senate," he said.

But other senators said staffers from other committees are pitching in. Sen. Mike Rounds, R-S.D., said staffers from Senate Finance and the Health, Education, Labor and Pensions Committee are drafting it.

Sen. Bill Cassidy, R-La., said he thought staffers from Finance and leadership were writing it up.

Sen. Bob Corker, R-Tenn., believed that only the leadership is drafting the bill and not any staffers from other committees.

"We can say the finance committee is [drafting it], the budget committee is or the HELP committee is but the leadership office is really writing the bill," he said Tuesday.

Lee made it clear that whoever is writing it, the process needs to be more open than it has been.

"If you're frustrated by the lack of transparency in this process, I share your frustration. I share it wholeheartedly," he said in his Facebook video.

Other senators have criticized writing the bill behind closed doors and bypassing the committee process, including Sens. Bill Cassidy, R-La., and Lisa Murkowski, R-Alaska. Democrats spoke well into the night on Monday blasting the lack of transparency through the process.

Sen. John Cornyn, R-Texas, the second-ranking GOP senator, aimed to clear things up. He told reporters Tuesday that the Senate Budget Committee is primarily writing the bill mainly because of reconciliation, the obscure pathway Republicans are using to take up the bill.

Reconciliation allows a bill to be approved in the Senate with only 51 votes as opposed to 60 needed to stop a filibuster. But to use reconciliation, a bill must reduce the deficit and only focus on spending and budgetary levels.

But Cornyn added that the committee is also getting help from Senate HELP and Finance committees.

Susan Ferrechio contributed to this story