The measure would also make it a crime to smuggle firearms out of the United States.
The Judiciary Committee has taken a lead in considering the gun violence issue following the shooting massacre last December at Sandy Hook Elementary School in Newtown, Connecticut, that left 20 children and six educators dead.
Leahy said there is no federal law now that defines either gun trafficking or straw purchasing as crimes.
The legislation will be taken up by the Judiciary Committee on Thursday as part of a package of four bills aimed at reducing gun violence. The others involve regulating assault weapons, enhancing school safety and requiring background checks for all firearm sales.
The proposed legislation would make it a crime to transfer a weapon when a person has "reasonable cause to believe" that the firearm will be used in criminal activity. It contains exemptions for the transfer of a firearm as a gift, or in relation to a legitimate raffle or contest.
While existing law makes it a crime to smuggle firearms into the United States, the Senate proposal would also ban the smuggling of weapons out of the United States. That provision is specifically aimed at the trafficking of arms across the Mexican border.