Hudson is eligible for salary arbitration, a process the club would like to avoid with him. The team has until Monday to decide whether to offer him arbitration. If it doesn't, Hudson would become a free agent.
"Hopefully we'll get something done in the next few days or over the weekend," Hudson said. "Obviously my wife and I have our roots set down here. We'd like to be here for the long run, and I'd like to have a long career with the Diamondbacks."
While the team would like to retain Hudson, who made $518,500 last season, the complicating factor is the raise he would be sure to get through the salary-arbitration process.
Hudson made just nine starts in 2012 before having Tommy John surgery and last June, just weeks before he was set to return, he reinjured his elbow during a Minor League rehab start and had to have a second Tommy John surgery.
The team faced a similar situation recently with reliever Matt Reynolds, who injured his elbow last June and had Tommy John surgery in September. Reynolds is expected to miss most, if not all, of the 2014 season, and he also was eligible for salary arbitration.
Reynolds and the D-backs agreed in October on a one-year $550,000 contract for 2014 with a $600,000 club option for '15.
Hudson is scheduled to play catch next week for the first time since his surgery.
"I'm looking forward to doing that and turning a corner," Hudson said. "My arm feels great."
This time around, Hudson is taking things slower. Whereas he began throwing a little more than four months after his first surgery, this time it will be more like six months.
"Just want to make sure I built up enough strength," Hudson said.
Steve Gilbert is a reporter for MLB.com. Read his blog, Inside the D-backs, and follow him on Twitter @SteveGilbertMLB. This story was not subject to the approval of Major League Baseball or its clubs.