Free-agent closer Fernando Rodney is in that group as the former Rays' All-Star hadn't arrived as of Tuesday and likely won't complete his physical until later in the week.
Two agreements were completed on Thursday, as the team announced the signing of left-hander Randy Wolf and right-hander Zach Miner to Minor League deals with camp invites. Wolf was expected to take the field with the rest of the Mariners pitchers and catchers for the first workout.
And Zduriencik acknowledged Tuesday that "there's probably a window to do something" still on the free-agent front, given the number of unsigned players still looking for employment as camps open this week in both Arizona and Florida.
"There's still pretty good players out there," Zduriencik said. "If you're looking for offensive players, starting pitchers, relievers, there are some guys out there. But every club has restrictions when you're at this point of the year. It isn't often easy for a club just to say, 'Give me $10 more million dollars or $15 million more dollars.' It just doesn't always work like that.
"Clubs have done their work, made investments and trades, taken on salaries and committed themselves. It's unfortunate some of these players are still there and that could be related to budget, could be related to asking prices or need. All those things tie into this."
The Mariners have talked throughout the winter with the agent for outfielder Nelson Cruz, who could provide another needed right-handed bat. And they've checked in as well on the remaining free-agent pitchers, a group that includes Ervin Santana and Ubaldo Jimenez.
But those players are still unsigned because they have risks or questions -- as well as Draft-pick compensation -- that so far have kept all teams from meeting their demands to date. Zduriencik talked all offseason of adding a veteran starting pitcher to his mix. So far he's brought in former Twins starter Scott Baker as a non-roster invite as he comes back from Tommy John surgery, as well as former Brewers first-round Draft pick Mark Rogers, who had shoulder problems last year.
Now he's added Wolf and Miner, two more vets returning from elbow issues. All those pitchers, as well as veteran reliever Joe Beimel, are on no-risk Minor League deals and will be given a chance to show where they're at this spring.
"Every guy we're bringing in has a legitimate shot to make this ballclub," Zduriencik said. "What I'd love is to have some of these guys with track records in the past be healthy and ready to go. That would make our decisions tougher, but also easier because if they become what they were or close to it, it would help us.
"We'll give them a chance to make this club. That's the challenge. There are no restrictions. No one is going to be held back because of contract restrictions or coming off an injury. If you come in here and compete and you're the best guy to make this club, you're making this club."
Wolf, 37, did not pitch in the Majors last season while recovering from his second Tommy John surgery. He posted a 13-10 record and 3.69 ERA in 33 starts for the Brewers in 2011, but then was 5-10 with a 5.65 ERA in 30 games for the Brewers and Orioles in 2012 before having surgery on his elbow.
Wolf was a 2003 All-Star with Philadelphia and has a career 132-117 record and 4.20 ERA in 376 games in 14 seasons with the Phillies, Dodgers, Padres, Astros, Brewers and Orioles.
Miner, who turns 32 in March, posted a 4.40 ERA in 16 games (three starts) for the Phillies last season and also was 5-6 with a 3.90 ERA in 27 appearances (12 starts) for the Phillies' Triple-A Lehigh Valley club.
Miner did not pitch in the Majors from 2010-12 after spending the previous four seasons with the Tigers. He is 25-22 with a 4.25 career ERA.