Lilly shares fell 40 cents to $43.30, and ImClone stock slipped 11 cents to $65.24.
The declines came on a morning when major stock indexes, including the Standard & Poor's 500, lost more than 2 percent of their values.
Late yesterday, after The Wall Street Journal and The New York Times reported Lilly's offer, ImClone issued a statement saying an unnamed suitor had "completed due diligence and made a proposal not subject to financing or further due diligence."
ImClone added that the suitor is a large pharmaceutical company that requested its name not be divulged until negotiations were completed.
The newspapers reported that Lilly had offered $70 per share for ImClone, citing unidentified sources familiar with the deal.
Indiana University business professor Larry Davidson said ImClone would offer Lilly a foray into a biotechnology business that could help it profit from advances in human genetic research.
However, much remains to be learned about the human genome and how to treat disorders, Davidson cautioned.
He added that drug companies have a bright future because aging baby boomers will need the products and developing nations will buy the products as their economies grow.
"It's certainly among the most promising industries," Davidson said.
Lilly's run at ImClone puts it in competition with one of its former executives.
The other company interested in buying ImClone, Bristol-Myers Squibb, is led by CEO Jim Cornelius, who was the chief financial officer at Lilly before he left in 1995 to become chairman of Guidant Corp., a Lilly spin-off.
Cornelius joined New York-based Bristol after Guidant was sold to Massachusetts-headquartered Boston Scientific Corp. in 2006 for $27 billion.
Bristol-Myers, which has a 17-percent stake in ImClone, upped its offer to $62 a share last month after staging an unexpected acquisition offer of $60 per share in July.