Bertrand hoping to force his way into Chelsea side
The 23-year old left-back has risen to prominence in the past 12 months with more regular appearances for the Blues and selection in the Great Britain Olympic team but he knows very well that pushing past England international Cole will be extremely difficult.
"Hopefully I'll go on and have a good season," he told BBC Sport.
"I played 15 games last season, so if I get 20-25 games it will show progress."
He added: "He's (Cole) is one of the best left-backs in the world.
"We have a good relationship. He's more than happy for me to play more games and pushes me on."