The 22-year-old first baseman also wants a Major League contract, which would require Alonso to be placed on the Reds' 40-man roster. Cincinnati is more willing to budge on that issue.
"That's something very important to him. It's something we will consider," Reds general manager Walt Jocketty said.
Major League clubs have until a midnight ET Friday deadline to sign players they drafted, or they lose the rights.
Jocketty, scouting director Chris Buckley and assistant GM Bob Miller are negotiating for the club with agent Greg Genske, who is serving as Alonso's advisor. Genske did not return calls seeking comment.
"I spent most of the day today dealing with it," Jocketty said of the talks. "I thought we made progress, but we're still a long ways apart. I'm waiting for them to come back to us. They haven't come off of their number."
The Reds are believed to trying to keep Alonso's contract close to the slot-system figure of $3 million.
Both sides have contingencies that help their leverage. Alonso has publicly said he's willing to return for his senior season at Miami or play in an independent league. The Reds would get a first-round compensation pick next year in the No. 8 overall spot, plus their original pick, if Alonso isn't signed.
"Right now, I'd say it's 50-50," Jocketty said of the chances the Reds would be able to sign Alonso.
Mark Sheldon is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.