"There's a bunch of teams in on Arthur," Horwits said. "We're going through the process of taking offers and giving them to Arthur and his family so they know where everybody stands. He's talked to some of the teams, in terms of general managers or managers, and he's just feeling his way through the process and getting down to where he can make a decision."
Cardinals general manager John Mozeliak was traveling on Tuesday and was not available for comment.
The Cardinals also have been negotiating with left-hander Trever Miller, free agent from the Tampa Bay Rays. That's been going on since Thursday, when Miller visited St. Louis for a physical exam.
Like Miller, Rhodes is tough on left-handed hitters. This year, pitching for Seattle and Florida, he held lefties to a .157 (11-for-70) average. Right-handed batters hit .309 (17-for-55) against him.
Overall Rhodes was 4-1 in 61 games with a 2.04 ERA. In his 25 games for the Marlins, he was 2-0 with a 0.68 ERA.
In his 17-year career, Rhodes, 39, stands 79-61 with 32 saves and a 4.23 ERA. Lefties have hit .221 against him, righties .245.
According to Horwits, his client plans to discuss the Cardinals' situation with Mozeliak soon.
"They're in the process of getting together. I don't know if they've officially talked yet," Horwits said.
Is there a time frame for Rhodes?
"It's not going to happen in the next day or so, but it could happen in the next week or so for sure," Horwits said. "We're going to go through the process of talking to teams and letting Arthur kind of whittle it down."
Dick Kaegel is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.