Last week, reports in the Italian media claimed Essien would leave current club Milan for Dallas when his contract expires in June.
The 32-year-old Ghanaian, who has started just five Serie A games under coach Filippo Inzaghi this season, has struggled to settle at Milan since joining from Chelsea last season, but, according to Clavijo, Dallas will not be his next destination.
"No, it's not accurate. No, it's not at all," Clavijo told the Dallas Morning News.
"We know Michael Essien of course. Everybody knows him, but we didn't offer anything at all."
Meanwhile, MLS journeyman and one-time Ghana international Dominic Oduro has moved from Toronto FC to Montreal Impact.
The 29-year-old striker has played for Dallas, New York Red Bulls, Houston Dynamo, Chicago Fire, Columbus Crew and Toronto in his nine-year MLS career.
After scoring just two goals in 24 matches for Toronto in 2014, Oduro will try his luck elsewhere in Canada.
"Dominic is an experienced player who has scored in our league and adds a different profile to our attacking options," Impact technical director Adam Braz said in a statement.
