Both fighters have agreed to the fight as of Tuesday, although contracts have yet to be signed.
MMA Junkie reported late Monday evening that McGee was forced to pull out of the fight due to a knee injury.
The Canadian Bongfeldt (21-7-1) fought to a draw in his UFC debut against Rafael Natal in December. The Ontario-native is unbeaten in his last eight fights.
Weidman (5-0) stepped in on short notice to defeat Alessio Sakara in his Octagon debut at UFC on Versus 3 last month.
UFC 131, headlined by Brock Lesnar vs. Junior dos Santos, airs live on pay-per-view on June 11 from Rogers Arena in Vancouver, British Columbia, Canada. The Bongfeldt-Weidman tilt is expected to air on the live Spike TV prelims telecast.