He registered 13 goals and nine assists for 22 points in 43 games with the Bruins this past season.
Blue Jackets GM Jarmo Kekalainen has been active on both the trade front and the free agent market thus far, looking to obtain at least one top-six forward.
Horton is a player the Blue Jackets are going "all in for," a source close to the situation told TFP late Wednesday.
It's unclear if Horton will meet with other teams in person, but he has attracted a lot of interest from other organizations.
In 591 career NHL regular-season games with the Florida Panthers and Bruins, Horton has accumulated 198 goals and 204 assists for 402 points.
Drafted third-overall by Florida in 2003, Horton was traded to Boston, along with Gregory Campbell, on June 22, 2010.