The Jackets' management, which includes senior adviser Craig Patrick, who selected Jagr fifth overall pick in the 1990 NHL Draft when he was GM of the Pittsburgh Penguins, was hoping to fill the hole left by Nash after he was dealt to the Rangers.
Jagr, 40, decided to sign a one-year, $4.5 million deal with the Dallas Stars on July 3 instead.
The veteran forward returned to the NHL last season and had a good year with the Flyers, collecting 19 goals and 35 assists for 54 points in 73 games.
Several teams looked to sign him after he played three years in the KHL, and many other clubs, including the Jackets, were also hoping to land him for the upcoming season.