The Northolme outfit are managed by Steve Housham, a former Scunthorpe player, and joins fellow former United players Jordan Thewlis, Andrew Pettinger, Lee Ridley, Darryn Stamp and Johnathan Williams.
"Looking forward to gaining some fitness on loan at Trinity," Godden wrote on Twitter.
"(It has) been a long and hard time out with injury. Time to enjoy again."
Defender Palmer, 19, has joined Blue Square Premier side Harrogate Town.
He has appeared twice for Scunthorpe, making his debut in the Johnstone's Paint Trophy win over Hartlepool in August before coming off the bench against Notts County in November.
Both loans are for initial one-month periods.