CHICAGO, Ill. — Talks aimed at keeping CME Group, Inc. and its 2,600 employees based in Chicago apparently have been going well, but the company has not made any final decisions about staying put.

The parent company of the Chicago Mercantile Exchange and owner of the Chicago Board of Trade and the New York Mercantile Exchange earlier this summer said it would consider moving because of what its CEO called the state’s “penal” tax structure.

The criticism came on the heels of the state legislature’s approval of an increase in Illinois income tax for individuals and corporations. “Our tax situation is untenable,” CEO Craig Donohue said at the time. “I don’t think CME Group is different from other companies” that consider relocating.

Up until last month, another such company considering moving its headquarters out of Illinois was heavy machine maker Caterpillar, Inc. Its chief executive said recently, though, that it would stay put, in part because Illinois leaders are willing to consider other changes to the state’s tax code.

As a result of the criticism from CAT and CME, along with other threats to bolt the state from Motorola Mobility and Navistar, state lawmakers conducted a series of four statewide tax code hearings through the end of August; a full report is expected next month.

CME’s key criticism is the state’s main tax on floor transactions is not tied to a particular location, even though they originate and take place electronically worldwide. Sources close to talks between Gov. Pat Quinn’s office and CME said Executive Chair Terry Duffy has met with Quinn on at least three occasions recently and suggested new ways to tax the company based on where the futures company transactions occur, according to Crain’s Chicago Business.

The new Illinois corporate tax rate is 7 percent, up from 4.8 percent. The increase is expected to cost the company an additional $50 million annually, a spokeswoman said.

CME has received formal proposals to relocate from leaders in five other states, including Indiana, Tennessee, Texas, Florida and Louisiana. “No decision has been made yet,” the spokeswoman said.

In addition to the corporate rate, Illinois also levies a property replacement tax only against corporations, pushing tax impact on companies to about 9 percent, among the highest in the United States. Also calling for changes in the state’s tax code are the Illinois Retail Merchants Assoc., the Illinois Chamber of Commerce, the Illinois Farm Bureau and Illinois Manufacturers’ Assoc.