Begovic joined the Blues from Premier League rivals Stoke on a four-year deal earlier this month following the departure of Petr Cech to Arsenal.
The move has raised questions of Begovic's motives, with Courtois firmly establishing himself as Chelsea's number one custodian in their Barclays Premier League title triumph last season.
However, Begovic, who had been Stoke's first-choice keeper for the past four seasons, is keen to press his claims at Stamford Bridge this term.
"I want to test myself against Thibaut, he's one of the best goalkeepers in the world but I believe in myself
I want to try and get as many games as I can," he said in several national newspapers.
"Hopefully every time I can show everybody what I'm all about and ultimately help this team
We all have to play our part and at a club like this I think you get to do so.
"There have been no guarantees
The challenge that's here, the manager and players was what attracted to me and that was a big part of my decision
"I'll back myself, absolutely
I'll be keeping my head down and working hard to see how I can help this team in the future."
Begovic, who ended a five-and-a-half-year association with Stoke, has already noticed the jump in quality on his arrival at Chelsea
"Even after the first week you can see the quality here and how they can improve you with the ÂÂlevels and demands here," he added
"It was difficult to leave Stoke after such a long time because of all the ties and relationships I had there
But this is definitely a step up."
Source : PA
Source: PA