A spokesman for Texas Pacific Group declined to comment.
Texas Pacific Group is also actively exploring a bid, these people said.
Further, Texas Pacific Group, an investment firm, was also negotiating with the company through Friday, but did not get to the same numbers.
The fund topped an offer by the Texas Pacific Group, which had structured a turnaround plan.
Zilog went public in 1991, but was acquired in 1998 by Texas Pacific Group.
Another buyout firm, Texas Pacific Group, is now said to be moving ahead with a financing plan.
It sold off the company in 1996 to a group lead by Texas Pacific Group; the company went public the next year.
The Texas Pacific Group would probably contribute some money, perhaps as much as half the purchase price, the person added.
The bidder is a company backed by the Texas Pacific Group, an investment firm.
J. Crew is a unit of the Texas Pacific Group.