I don't remember there being another offer. As I recall, Bill Wrigley was facing major inheritance tax problems since both his parents had died a couple years before. My recollection is that the Tribune swooped in and bought the team, which was losing big money at the time.
The reason the Tribune was interested was because the Cubs had been talking with Eddie Einhorn about joining up with the White Sox in Einhorn's new pay-TV venture that would broadcast Chicago sports. The Tribune was spooked because the Cubs were worth a lot to WGN radio and WGN-TV as programming, and that would be lost if the Cubs got on the pay-TV bandwagon.
I found a New York Times article
describing the sale. It doesn't say anything about other offers being considered by Wrigley. Maybe somebody else remembers another suitor, but I don't think there was; the Cubs were a distressed property at that time (now they're just a grossly overpriced distressed property