The newspaper, without naming sources, said the two sides are set to finalize the deal for the reigning Vezina Trophy winner after the conclusion of the ongoing 2013 NHL draft in Newark, N.J.
Bobrovsky was in line to become a free agent at the end of this week.
The 24-year-old Russian goalie emerged into a star this past season, leading the Blue Jackets' push to make the playoffs for only the second time in franchise history.
The squad ultimately fell short despite Bobrovsky's 21-11-6 record with a 2.00 goals-against average and four shutouts in 38 games.
He has racked up a 63-34-16 mark with a 2.49 GAA and .917 save percentage over three years with the Philadelphia Flyers and the Blue Jackets.