Both Narron and general manager Wayne Krivsky confirmed there have been talks with Loretta's agent, Bob Garber.
"I've talked to his agent, but I've talked to a lot agents," Krivsky said.
Loretta is a career .299 hitter with a .363 on-base percentage but offers little power. He batted .285 with five homers and 59 RBIs with the Red Sox in 2006.
The Reds need a right-handed hitter to replace free-agent infielder Rich Aurilia, who signed a two-year contract with the Giants on Monday.
A wide net has been cast.
Shea Hillenbrand, Craig Wilson and Eduardo Perez are among lower-priced free agents the Reds have targeted on the market. The preference is to get someone who can play first base and/or the outfield. Loretta, Hillenbrand, Wilson and Perez all have varying experience at first base.
"Now that we've lost Aurilia, we're trying to find someone who can do some of the things he can do and replace him as best we can," Krivsky said. "We have a list of players we're interested in and we'll see if we can find something that works for them and works for us."
Meanwhile, Krivsky has fielded his share of trade inquiries but avoided specifics.
"It just comes down to having a match. It's not rocket science," he said. "Coming in here, you're not going to have a match with 29 other teams. You don't have time to do all that. You want to concentrate on the teams you think you have a match with."
Building a case: The Reds have yet to file a grievance with Major League Baseball against the Nationals over July's Gary Majewski trade.
But one appears to be coming soon.
"It's in the hands of attorneys," Krivsky said. "There's a lot of work that goes into it."
Krivsky felt that general manager Jim Bowden and the Nationals did not deal honestly in the July 13 eight-payer trade that sent Austin Kearns and Felipe Lopez to Washington for Majewski, Bill Bray and Royce Clayton.
After he produced disastrous results shortly after the trade, Majewski revealed the Nationals knew he had a sore shoulder all season and gave him a cortisone injection. The Reds, who did not give the reliever a physical while relying on Washington's medical reports, felt the right-hander was damaged goods.
"We'll put our case together as best we can -- dotting the I's and crossing the T's -- and turn it in and wait for a decision," said Krivsky, who would not say what type of relief he was seeking from MLB.
In a new development, Nationals head trainer Tim Abraham resigned Monday, citing family reasons. A Nationals spokesman insisted Abraham's departure had nothing to do with the Majewski issue.