The songs would have to be properly registered at a US PRO (such as ASCAP, BMI, SESAC) as well as other US collection agencies like The Harry Fox Agency and Music Reports.
If the songs were written by a non-US citizen with no US Social Security Number, they can still apply for affiliation at a US PRO, however they would need to mail a physical paper application to the PRO along with a completed W-8 BEN form as opposed to submitting the application online.
Once the foreign writer is affiliated at the US PRO, you can register the writers’ works, making sure to note your publishing interests for each work. This will ensure that the writer will receive writer royalties directly from the PRO while the publishing royalties will be paid to the publisher noted.
Depending on how your publishing deal is structured, you may also be eligible to receive a portion of the publisher’s share of performance royalties.