Jason Churchill of Prospect Insider and ESPN.com, reported Tuesday that according to a source, the Mariners are "working pretty hard" on an extension and "may have something done right before or after the World Series."
Hernandez currently has two years and $40.5 million remaining on the five-year, $78 million deal he signed in 2010.
Zduriencik maintained his policy of not discussing contract negotiations, though he has repeatedly maintained the Mariners are not interested in trading their 26-year-old ace.
"Felix has made it clear he'd like to stay here, and we've made it clear we'd like him to stay," Zduriencik said. "That's all I'm going to comment on that right now."
Zduriencik's biggest offseason challenge is beefing up the club's offense in order to help Hernandez and the rest of a pitching staff that had the lowest run support in the American League for three straight years.
"We're going to be open to do whatever we can to improve the club," Zduriencik said. "Obviously, we'd love to get a bat some way, some how, whether through free agency or a trade. I have some flexibility on where that guy could play.
"That's just one of our priorities, to bring in a veteran presence, someone who can help us," he said. "You never know what's around the corner that can help in whatever area possible."
Zduriencik is looking forward to seeing top 2012 Draft pick Mike Zunino in the Arizona Fall League, though he's not banking on the young catcher being in the immediate plans next spring, despite a strong showing in Class A Everett and Double-A Jackson after signing in July.
Zunino just arrived in Peoria after getting married on Saturday. He didn't play in Peoria's opener on Tuesday, but was scheduled to be the designated hitter in Wednesday's game in Surprise.
"He'll be invited to Spring Training as a non-roster invite," Zduriencik said. "But for anybody to expect the kid to play half a season [in the Minors] and make the club, that would be extraordinary. You never count it out, but the best thing is to let him come in and see where things fall."
Zduriencik currently has catchers Jesus Montero, John Jaso and Miguel Olivo on the 40-man roster. Olivo will become a free agent unless the Mariners trigger a $3 million club option that would bring him back for one more year.
Zduriencik declined to say whether the team would look for outside catching help this offseason.
"With our current situation with the three guys on the roster, we'll look at that and other options," he said.
Montero's future is a little uncertain. He played 78 games at designated hitter and 56 at catcher as a rookie and there's some thought he could fit into the mix at first base down the road. The Mariners have asked him to do some things this offseason to work on his speed and athleticism, but Zduriencik wasn't ready to commit to the 22-year-old as a first-base option heading into next spring.
"He could be some part of that, but right now you have to look at him as a DH/catcher," Zduriencik said. "That's a hard question to answer right now. A lot depends on what he does this winter. That's not something we're counting on right now."
The Mariners have numerous questions to answer this offseason, including whether first baseman Justin Smoak's September surge was enough to warrant his return as the starter and if Franklin Gutierrez can be counted on in center field.
Zduriencik was encouraged by Smoak's late run, but acknowledged "my eyes and ears are wide open this offseason" when it comes to bringing in competition at any position.
"We're going to try to make this club better and where players stand is just dependent on what we do," he said. "Right now, he probably has the upper hand. But he's not a proven commodity. He's played great defensively and you really like what you saw in September, but it's a long season and guys have to maintain that. We'll see what happens."
Gutierrez carries similar uncertainty after playing just 40 games this season and 92 in 2011 due to a run of health issues.
"That's a tough one," Zduriencik said. "You'd love to be able to count on him for 140-150 games, but recent track record tells you that you have to keep options open."
Gutierrez has one year at $7 million remaining on his contract. The Mariners are hoping he can play winter ball for about a month this offseason to accrue playing time.
Free agency begins the day after the World Series ends, so there's some time before roster reconstructions begin. But Zduriencik has plenty on his plate already, including spending time this week with manager Eric Wedge looking at youngsters in Arizona.
The team also is in the process of hiring a new hitting coach to replace Chris Chambliss, whose contract was not renewed.
"We're having a lot of dialogue and would like to get that done sooner than later, so that person can get familiar with our guys and what we're doing as soon as possible," Zduriencik said.