"I don't know if I want to handicap that," Jocketty said.
Developments have been slow since December, when Cueto and agent Bryce Dixon set a deadline of Opening Day to complete a new contract. Entering the $10 million option year of his current deal, Cueto will explore the free-agent market if he is not signed.
"We've been busy with other things. We'll take a good look at it before camp and see if we can sign him or not," Jocketty said.
There is no doubt that locking down Cueto will be a challenge for a small-market Reds club already saddled by the big contracts of Joey Votto, Homer Bailey and Brandon Phillips.
Cueto, a 20-game winner and the National League's leader in innings and strikeouts last season, likely will be pursuing a mega contract in the neighborhood of the six-year, $155 million contract Jon Lester signed with the Cubs last month.
There are other contract negotiations on the horizon for the Reds, who have five players eligible for arbitration: third baseman Todd Frazier, catcher Devin Mesoraco, reliever Aroldis Chapman, starting pitcher Mike Leake and shortstop Zack Cozart.
Jocketty didn't expect much progress toward signing the players until arbitration figures are exchanged. That is scheduled to happen league-wide next Friday.
"This week was more about preparing for the cases," Jocketty said. "I don't think we'll do a lot of discussions until next week."
Meanwhile, the Reds are still pursuing additions for the bullpen and bench -- a process Jocketty characterized as "slow." After Cincinnati claimed right-handed pitcher Keyvius Sampson off waivers on Thursday, it has a full 40-man roster.
That means that any free agents signed by the Reds would likely get a Minor League contract with an invitation to big league camp.
Mark Sheldon is a reporter for MLB.com. Read his blog, Mark My Word, and follow him on Twitter @m_sheldon. This story was not subject to the approval of Major League Baseball or its clubs.