The chairman of the Senate Rules Committee, Jeff Mullis, said the committee will release an amended version of House Speaker David Ralston's plan on Thursday. Mullis said he hopes to have a floor vote Friday.
House and Senate leaders are in talks about how to resolve political disagreements over the plan.
Ralston has proposed prohibiting lobbyists from spending money on individual lawmakers, though lobbyists could still spend on groups of lawmakers like committees, caucuses or delegations.
Mullis said Senate lawmakers believe a $100 cap would be preferable. Senate lawmakers have also criticized proposals from Ralston that would force more people to register as lobbyists.