Speculation over the last few months had suggested that England international Cole would be allowed to leave Stamford Bridge on a free transfer at the end of the season, thus leaving Bertrand as the only recognisable left-sided defender at the club.
However, despite having competition for his place, Bertrand has confessed that he is glad to have Cole around.
"I have said from the start that he deserves another contract," Bertrand said. "We have a good relationship. I'm always learning and there is no one better to learn from.
"He has given me plenty of advice over the years. The best advice is not so much what he has given me verbally but just watching him every day and the way he goes about his business.
"[Our relationship] reflects in our performances when we play together and I am in front of him at left midfield. It is probably the natural progression to share the left-back role, but I don't pick the team."
Bertrand has made 23 appearances in all competitions this season.