The news comes just a week after another club from Russia's volatile south, Anzhi Makhachkala, signed the veteran Brazilian defender Roberto Carlos on a two-year contract worth a reported two million dollars.
The Tvoi Den daily said direct talks between the Russian Premier League outfit and 34-year-old Ronaldo will take place in Grozny on March 8, when some members of Brazil's 2002 World Cup-winning side arrive for an exhibition match.
It is thought Grozny are prepared to offer Ronaldo an 18-month contract.
Ronaldo, who announced his retirement last week, has been appointed to help co-ordinate Brazil's hosting of the 2014 World Cup.
"Ronaldo has recently announced the end of his football career, and this is what Terek management's is using," Tvoi Den quoted one Russian football agent familiar with the situation as saying.
"Ronaldo has already been invited to come to Chechnya, but there has been no response from the Brazilian," the agent said.
Terek have been raising their profile since January, when they stunned the football world by announcing the signing of Dutch football legend Ruud Gullit as manager.
The club finished in the lower rungs of Russia's top division last year and have only one Russian Cup to their credit.
But they enjoy immense support from the republic's iron-fisted ruler, Ramzan Kadyrov, with the vast Chechen business diaspora living in Moscow and other major cities providing them with financial support.
Gullit has vowed to attract international talent to the youthful side in a bid to make them the new dark horses of Europe, setting himself the goal of qualifying Terek for the Europa League within the next few years.
The Chechen government announced last week that it had invited stars such as Kaka, Ronaldo and Ronaldinho from Brazil's 2002 World Cup winners to play an exhibition match against "team Kadyrov".
"If everything goes according to plan, the residents of Chechnya will be able to see such football greats as Kaka, Ronaldo and Ronaldinho on the pitch," Chechen Sports Minister Haidar Alkhanov said in a statement.
There has been no confirmation of such a match in Brazil, which would be played in a stadium that in 2004 witnessed a bombing that killed Akhmad Kadyrov, the current president's father and predecessor as head of Chechnya.
The Chechen side's season opens on March 13 when they play 2010 champions Zenit Saint-Petersburg, who finished 35 points and 12 places above Terek last season.
