With Frank Fielding challenging Adam Legzdins for the number one jersey at Pride Park, the Rams are currently blessed with options between the posts.
Atkins this week returned from a temporary spell at Burton and Rams boss Nigel Clough is keen for the 23-year-old to get some more matches under his belt.
Deeney, 29, meanwhile, has not made a first-team appearance since May 2010 following an injury-plagued two-and-a-half years.
"We will be circulating their names to clubs letting them know that they are available," Clough said.
"It's a luxury for us having two great goalkeepers in Adam and Frank, so hopefully there will be an opportunity for Ross and Saul to get some games.
"We don't like seeing players who are desperate to play sat on the bench. I don't think it's good for them and it's not good for us in the long run."