“We’re in a discussion about what to do on the gun issue in the wake of these horrendous shootings," McConnell said during an interview with radio host Hugh Hewitt.
At least 35 people were killed in mass shootings in El Paso and Odessa, Texas, and Dayton, Ohio, in the month of August alone.
"I said several weeks ago that if the president took a position on a bill, so that we knew we would actually be making a law, and not just having serial votes, I’d be happy to put it on the floor,” McConnell said.
McConnell said the Trump administration “is in the process of studying what they're prepared to support, if anything.”
McConnell refused to call the Senate back into session from its annual August recess last month to consider gun legislation, despite numerous calls from Democrats to do so.
"We'd just have people scoring political points and nothing would happen," McConnell said at the time.
But McConnell says he is on board with passing some sort of legislation in September that has bipartisan support in both chambers of Congress, as well as the president's support.
“If the president is in favor of a number of things that he has discussed openly and publicly, and I know that if we pass it, it’ll become law, I’ll put it on the floor."
But it's unclear which measure the White House supports and if it would include implementing universal background checks or simply expanding on current background checks.
Congress has not passed any sweeping gun reform legislation since the 1990s. Lawmakers have tried and failed numerous times, notably after the 2012 shootings in Newtown, Connecticut, in which 20 school children were killed by a gunman.
Other proposals the White House is potentially weighing include a federal grant program that would assist states in implementing a “red flag” law, which Sens. Lindsey Graham, R-S.C,. and Richard Blumenthal, D-Conn., support. The state laws typically permit police or family members to petition a state court to order the temporary removal of firearms from a person who may present a danger to others or themselves.
The White House could also consider two background check bills passed by the House in February.
One of the bills would establish new background check requirements for firearm transfers between private parties. The other bill would extend the review period for the FBI to complete its background checks for gun purchases from three days to 10 days.
GOP Sen. Pat Toomey of Pennsylvania told ABC's "This Week" on Sunday that he's unsure where the president currently stands.
"I have spoken with the president repeatedly and recently about this topic. He is very interested in doing something meaningful," Toomey told ABC's Chief Global Affairs Correspondent Martha Raddatz.
"He hasn't endorsed a specific bill. I think that would be premature. But he and I have an ongoing conversation about this. I know other interested senators are participating in that conversation. And our staffs, including the White House staff, are very seriously pursuing this," Toomey said.