The suit pertains to the title deed for the land in Luque, just outside the capital Asuncion, said Alejandro Dominguez.
"We asked for more information to see if our deed is or isn't legitimate and the answer I got was that it is totally legitimate," Dominguez said.
"But unfortunately this is something that threatens CONMEBOL's presence in Paraguay."
The confederation was also facing nine other suits, many from former employees, he added.
CONMEBOL has been hard hit by the recent FIFA corruption scandal with Dominguez's three predecessors and officials from all 10 member nations among those indicted.
A U.S. investigation into more than $200 million in bribes and kickbacks sought and received by football officials for marketing and broadcast rights to tournaments and matches has led to more than 40 individuals and entities being charged.
Paraguayan Dominguez, 44, was elected in January and has vowed to restore CONMEBOL's credibility.
(Writing by Andrew Downie; Editing by Peter Rutherford)
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