Tampa Bay Rays pitcher Jeff Niemann, infielder Ryan Roberts and outfielders Sam Fuld and Matt Joyce were among 133 major league players who filed Tuesday for arbitration.
The Rays and the players have until 1 p.m. Friday to exchange numbers for a 2013 contract.
Rays executive vice president of baseball operations Andrew Friedman said deals could still be reached before Friday's deadline.
"I just don't have a good feel. Very well could, just don't know yet," he said.
Friedman also said the Rays' quest to add two relief pitchers and one or two bats continues.
"Continuing to canvas the market for free agents and trades and seeing what lines up that makes us better," he said of the team's offseason objectives. "We certainly don't need to do anything. We feel comfortable with the guys that we have in house.
"But that being said, obviously we'd like to continue to get better. By doing that, we also add more depth, which is a good thing."
Friedman said he is still searching for a traditional designated hitter but doesn't feel a pressing need to add one.
"Point is, there's a scenario where you have one position player who's not a DH and you just rotate a bunch of guys through to get them off their feet, and then there's scenarios where you add a more traditional DH," he said.
"We're just going through all those scenarios."