SARASOTA, Fla. — The Cincinnati Reds wrapped up training camp with an overture to Gary Sheffield and a lingering question about the last opening in their starting rotation.

Manager Dusty Baker said Thursday that he’s interested in adding Sheffield — a friend for many years — to the roster. The trouble is that he can’t offer regular playing time to the 40-year-old free agent, who is hoping for a full-time job and a multiyear deal.

Baker got permission from general manager Walt Jocketty to call Sheffield and see if he would consider the Reds, who don’t have a starting job open. Sheffield, who was released by the Detroit Tigers on Tuesday, could start in left field when the Reds are facing a left-handed pitcher, fill in at first base on occasion and pinch-hit.

‘‘I don’t even know if we’re in the running or not,’’ Baker said. ‘‘He wants playing time.’’

How much could Baker give him?

‘‘I don’t know,’’ he said, adding, ‘‘I wasn’t going to lie to him.’’

Sheffield also has been contacted by the Philadelphia Phillies. Though Philadelphia’s outfield is set, Sheffield could sign on for a reserve role with the defending World Series champions. The Reds are coming off eight straight losing seasons.

Agent Rufus Williams said several clubs had contacted him about Sheffield, who cleared waivers on Thursday afternoon. He didn’t have a self-imposed deadline for accepting an offer.

‘‘It’s important that Gary be on the field,’’ Williams said. ‘‘It’s important that he play. It’s his intent to play beyond this season.’’

Sheffield was Detroit’s designated hitter before the Tigers released him on Tuesday. Shoulder injuries and other problems limited him to 114 games and a .225 average last season. He batted .178 in spring training.

Sheffield has 499 career homers, one shy of becoming the 25th player to reach a milestone. The Tigers will have to pay the difference between whatever Sheffield signs for with another team and the $14 million he was owed on his contract with Detroit.

Baker’s long-standing friendship with Sheffield — they met years ago through mutual friends from California — is the biggest thing in Cincinnati’s favor.

‘‘I’m sure he has some offers,’’ Baker said.

While they wait for Sheffield to make up his mind, the Reds have to come to a decision on right-hander Homer Bailey, a former first-round draft pick who pitched like one this spring.

Right-hander Micah Owings made himself the front-runner for the fifth starter’s spot by impressing early. The 22-year-old Bailey extended the competition by showing that he has started to develop into the pitcher that the Reds envisioned. Bailey struck out eight in six innings of a 7-2 loss to the Astros on Wednesday.

A day later, the Reds were still noncommittal on whether it will be Owings or Bailey filling out the rotation.

‘‘We’ve got to confer before we make any call,’’ Baker said, referring to the front office. ‘‘That’s how you do things. It’s a joint thing. If not, why do you have advisers if you don’t need them, if you don’t use them?’’

It will be their toughest decision of spring training.

Bailey was the seventh overall pick in the June 2004 draft and dominated in the minors, but struggled after he was called up in 2007. He had a chance to win the fifth starter’s spot last spring, but had trouble throwing strikes — 16 walks in 19 innings — and started the season at Triple-A Louisville. Later, he went 0-6 in eight starts for Cincinnati with a 7.93 ERA.

The right-hander refined his delivery in the offseason and came to camp with more confidence and much better control. He has walked only four batters all spring.

If the Reds keep Owings as the fifth starter, they could use Bailey in long relief — a role that means he won’t get to pitch regularly — or send him back to Louisville to keep refining his delivery. Or, they could decide it’s time to give Bailey the job.

By pitching so well, Bailey turned it into a tough decision.

‘‘That’s kind of what I had planned on at the beginning of this spring,’’ Bailey said Thursday. ‘‘Now it’s just kind of an unfortunate waiting game and just see what happens. But that’s good. That means other guys are doing well, too. So that’s good for everybody.’’