Toronto has Oliver under contract for another year after the club exercised his $3 million option earlier this offseason. Even if that money does eventually come off the books, there's no guarantee it will be allocated to another player.
Anthopoulos said it's unlikely the Blue Jays would make another splash on the free-agent market because the club already finds itself beyond its original salary expectations.
The acquisitions of Josh Johnson, Mark Buehrle, Jose Reyes, Emilio Bonifacio, Melky Cabrera and R.A. Dickey have made it difficult to provide any extra funding to the on-field product.
"We blew so far past where we were supposed to be," Anthopoulos said of his payroll. "Darren was an exception. We exercised the option at the beginning of the offseason; payroll commitments were so different back then.
"Obviously if Darren was to choose to come back, we would certainly honor that; we'd be thrilled to have him. But that money is Darren Oliver money. It's not go-get-another-player-or-reliever money."
Pitchers and catchers are set to report to Spring Training on Feb. 13, and Oliver must make his final decision before then. He will either return, retire or be placed on the restricted list, and he appears free to use all of the time between now and then to make up his mind.
The one thing Anthopoulos doesn't appear inclined to do is offer Oliver more money to stick around. Oliver's agent Jeff Frye recently made that request and told MLB.com that if the demands are not met, Oliver would prefer to be traded to the Rangers, who play near his family's home.
"It's going to take a lot more money for Darren to play in Toronto than play in Texas," Frye said. "We're waiting on the Blue Jays to pay him what he deserves. If not, we have asked them to trade him to Texas if the Rangers are interested."
It's an obvious negotiating ploy and one that comes with a fair bit of leverage, considering Oliver seems just as willing to walk away from the game if his demands are not met. But Anthopoulos also has his own fair share of leverage in that he has the ability to simply tell Oliver he can either play in Toronto or not at all in 2013.
Anthopoulos declined comment on potential trade talks but firmly stated he wouldn't make a trade just to accommodate the wishes of a player.
"I can tell you when we make trades, we make trades that we think is fair value," Anthopoulos said. "If there's a deal we think makes our team better -- and really at this stage, makes our big league team better -- we'd explore it with any player under contract, but we're not looking to make our team worse or the organization worse."
If Oliver does eventually retire, the Blue Jays have a trio of left-handers that will compete for a pair of jobs in the bullpen. Brett Cecil and Aaron Loup are in the mix, while J.A. Happ prefers to start but will be forced to compete for a job as a reliever because of Toronto's recent additions to the rotation.