Chief Executive Officer Rex Tillerson is among people in Bartonville, a Dallas surburb, who filed a lawsuit against construction of the 160-foot-high tower, complaining it would create "a noise nuisance and traffic hazards," the Journal reported Thursday.
The tower would be located near an 83-acre ranch owned by the Tillerson family.
The Journal said the issue is related to local zoning ordinances.
An Exxon spokesman said company directors weren't told of Tillerson's involvement in the lawsuit. The spokesman said the company itself "has no involvement in the legal matter."
Texas has some of the largest shale oil and natural gas fields in the United States.
Critics of hydraulic fracturing, the controversial drilling practice known as fracking, say it's too water-intensive and some of the chemicals used in the process may be a threat to the environment.
An investigation by the Weather Channel found the air quality monitoring system in Texas is "so flawed that the state knows almost nothing about the extent of the pollution" from shale operations.
Notable deaths of 2014 [PHOTOS]