Deeney, 26, is a free agent after leaving Football League newcomers Burton. He has been training with Derby and went on the Rams' pre-season tour of the south west last week where he played 90 minutes in the goalless draw against Torquay.
Manager Nigel Clough, who is still also interested in signing 21-year-old keeper Fielding from Blackburn, said: "There is no change on Frank Fielding but Saul we will get signed up this week.
"So if nothing happens, we will go with Stephen Bywater and Saul Deeney in the first game (of the Championship season) against Peterborough."
Meanwhile, Derby are no closer to agreeing a deal with Crewe for right-back John Brayford, but Clough revealed he is also in talks about bringing two loan signings to Pride Park.
"We are still waiting on a couple of departures which may well trigger us," he added. "But we are also awaiting a decision on two loan players coming in, two young players on long-term loans, and we hope to get at least one of those."