Braves general manager Frank Wren and Hudson's agent, Paul Cohen, began negotiations on Thursday and they are expected to continue talking over the course of the next couple of days.
"We just kind of got the ball rolling," said a source with knowledge of the negotiations.
Hudson has provided every indication that his primary desire is to stay in Atlanta. Last week, the 34-year-old right-hander reiterated that he is not even thinking about the contents of his current contract, which includes a $12 million option and $1 million buyout for the 2010 season.
"Truthfully, I've never even thought that the option was an option," Hudson said last week. "I'd rather have an extension than an option."
Specifics about the early extension talks weren't revealed. But it is believed the Braves would be comfortable providing Hudson an offer of three years worth $27-29 million.
Hudson, who went 2-1 with a 3.61 ERA in the seven starts that he made after returning from Tommy John elbow reconstruction surgery this year, may be looking to also gain an option for the 2013 season.
"I feel like my arm is stronger than it has been in a long time and that some of my best years are ahead of me," said Hudson, who will turn 35 in July.
If the Braves are able to complete an extension with Hudson, they'll likely accelerate their efforts to trade either Kenshin Kawakami or Derek Lowe.
With three years and $45 million remaining on his current contract, Lowe will be difficult to move. Even if a pitching-hungry, big-market club was interested in the veteran sinkerballer, who notched a team-high 15 wins this year, the Braves would likely have to eat a portion of his contract.
During last week's organizational meetings in Florida, the Braves discussed the various ways that they could handle their surplus of starting pitchers. With Tommy Hanson and Jair Jurrjens, they have a pair of top-of-the-rotation 23-year-old right-handers, who could form a strong duo in Atlanta for many years to come.
Thoughts about trading Javier Vazquez decreased as he completed his impressive season this year. Still after going 15-10 with a 2.87 ERA this year, the 33-year-old right-hander positioned himself as the starter who would provide the greatest return if the Braves were to decide that they need to move him.
Mark Bowman is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.