Cole injured his hamstring during the club's FA Cup quarter-final victory against Manchester United at Stamford Bridge on Easter Monday.
And that has given Bertrand a chance to impress interim boss Rafa Benitez with seven games to come in three different competitions in a busy April.
The Blues face home games against Rubin Kazan in the Europa League on Thursday and Sunderland in the Premier League at the weekend before taking on Manchester City at Wembley for a place in the Cup final, and Bertrand is determined to make an impression.
"It's down to me to keep training well, keep my performances up to a level and keep pushing and pushing until the time comes," he told the club's official website.
"He (Cole) has been a focal point for my career even before he was at Chelsea.
"He was someone I used to watch when I was younger and having him here at Chelsea has been a good chance for me to see first-hand how he goes about his work day in, day out and he provided a good basis for me to plan around.
"Personally it's a chance for me to come in now and play in the next few games, but it's just important to focus on the next game and make sure we get the right results."