The Trotters are currently rock-bottom of the Championship with just eight points from 11 games, and their tally of nine goals is one of the worst in the division.
And it’s now claimed that Lennon is eager to address this lack of firepower with a move for released West Ham forward Cole.
The 32-year-old has been without a club since the start of the summer, but is currently training with Celtic in a bid to earn a contract with the Glasgow giants.
Speaking about the seven-cap England international, Lennon said:
“Carlton’s a free agent and he’s a striker, so it’s definitely a possibility.
“We’re still looking to add one or two and it’s no secret that I want a centre-forward.”
Bolton have also been linked with Northern Irish hero Kyle Lafferty and Gary Hooper of Norwich – Lennon signed the latter while in charge of the Bhoys.