Her proposal, coming in the wake of the horrific massacre at a gay nightclub in Orlando by a gunman pledging allegiance to ISIS, would bar gun sales to those on the government's no-fly list.
The Senate is scheduled to vote Monday on two competing proposals -- one from Democratic Sen. Dianne Feinstein of California and one from GOP Sen. John Cornyn of Texas -- that also seek to prevent those with potential terror ties from buying guns. But similar versions by those senators were rejected in December and neither is expected to pass next week.
"Rather than doing Groundhog Day, I think it's time for a new approach and a more targeted one," Collins told reporters Thursday.
In addition, senators will also vote on one Democratic and one Republican proposal addressing background checks for gun sales, but members of both parties admit they are unlikely to be approved.
Senate Majority Leader Mitch McConnell and Senate Minority Leader Harry Reid have not ruled out Collins' proposal, according to multiple sources, but it's unclear whether it could get enough support from either side to clear the 60-vote threshold it needs to pass in the Senate.
The current draft of Collins' legislation -- which is being cosponsored by six senators, her office says -- bars sales to any individual on the no-fly list and includes an appeals process for those who are denied the ability to buy a gun.
If the buyers prevail in court, the government would be required to reimburse their legal fees.
The bill also includes a five-year "look back" provision that Collins said is specifically aimed at preventing what happened with the Orlando shooter, Omar Mateen. The proposal would require the background check database to send an alert to the FBI when any individual who had been on the no-fly list in the last five years buys a gun so law enforcement agencies can re-open a review and consider new surveillance.
Mateen was on a watch list and was the subject of FBI investigations, but after his case was closed, there was no requirement to flag those purchases.
Another key dynamic is whether the National Rifle Association weighs in on the proposal. If they endorse it, McConnell could move ahead with a vote, but Democrats will likely worry it goes too far, and peel off. If the pro-gun rights group opposes the plan it is unlikely to get a substantial number of GOP votes.
Collins told reporters Thursday she is working with Sen. Jeff Flake, R-Arizona, Sen. Lindsey Graham, R-South Carolina, and Sen. Kelly Ayotte, R-New Hampshire, and had some "expressions of interest" from some Democrats. But her office declined to say on Friday who would co-sponsor the bill when it is introduced on Monday.
Asked about the prospects that her own leaders will allow a vote on it, Collins said, "That remains to be seen."