Diamondbacks president Derrick Hall told MLB.com on Monday that the two sides have had discussions about Johnson, but Yankees general manager Brian Cashman did not return a phone call Tuesday and was unavailable for comment.
One baseball official with knowledge of the situation placed the odds at "65-35" that the Yankees would deal Johnson, who has won 17 games in each of his two seasons in New York.
The official, who was granted anonymity because of the sensitive nature of the talks, said that the Yankees would certainly be willing to part with the five-time Cy Young Award winner for the right package of players and/or prospects.
"If it makes sense, it will get done," said the official. "But it isn't something that has to get done."
On Monday, Hall said that Diamondbacks GM Josh Byrnes had held "significant talks" with the Yankees, but added that the two teams had not been able to put the right mix of players together to complete a deal.
Johnson has a full no-trade clause, but would likely be willing to waive it to return to Arizona. As of Tuesday, Johnson had not made an official trade demand to the Yankees.
The official said that the Padres have inquired about Johnson as well; reliever Scott Linebrink is believed to be the San Diego player that interests the Yankees the most. The Dodgers and Angels have also been mentioned in published reports as potential suitors, but it is unknown whether Cashman has spoken with either Los Angeles club.
Alan Nero, one of Johnson's agents, told the Associated Press on Monday that he spoke that day with Cashman, who informed him of preliminary discussions with several teams regarding the left-hander.
"As far we know, there's nothing going on significant enough for us to become a part of it," Nero said. "I think Brian is just doing his job."
The Yankees have Johnson penciled into a rotation with Chien-Ming Wang, Mike Mussina, Andy Pettitte and either Kei Igawa or Carl Pavano. Should the Yankees deal Johnson, it would open a spot for the team to pursue Barry Zito, the top free agent remaining on the market.
The official said that the Yankees aren't likely to pay Zito the $100 million over six years that he is looking for, but if Zito and his agent, Scott Boras, offer them a discounted deal -- just as Boras client Carlos Beltran did two years ago before signing with the Mets -- the Yankees could have some interest.
The Yankees could also be looking to trade Johnson to open a spot in the rotation -- as well as some space on the payroll -- for Roger Clemens, who has yet to announce his plans for 2007. However, New York could pursue Clemens even if Johnson is still on the team.
"I would think Roger would be in the mix no matter who is in [the Yankees'] rotation," the official said.
Should the Yankees trade Johnson, they also have some internal candidates in the farm system who could battle for a rotation spot, including Humberto Sanchez, Jeff Karstens, Darrell Rasner and top prospect Philip Hughes.
Mark Feinsand is a reporter for MLB.com. Steve Gilbert contributed to this report. This story was not subject to the approval of Major League Baseball or its clubs.