The summer recruit also says the additions to the squad have made them a good team.
The 'keeper joined on a free transfer from Bolton last month as one of the first of several new faces that have arrived at Anfield this summer.
He is well aware he has been brought in as a replacement for Brad Jones, who departed the club when his contract came to an end this summer and was firmly stuck as number two behind first choice Simon Mignolet during his time at the club.
And Bogdan is well aware it will not be easy to supplant the Belgian in the Liverpool goal.
“I would like to challenge for the number one spot but of course it's not easy,” he told lfctour.com.
“Simon has been here for two years and he's fantastic. He's really a top 'keeper. I have a chance; I'm lucky to work with him every day and make myself better as well.”
Targeting silverware next season
The 'keeper also says that he and the squad are targeting a piece of silverware next season.
The Reds were highly disappointing last season as a fine second half of the campaign could not make up for a poor start and they finished sixth in the table.
Aston Villa and Chelsea also beat them in both their semi-final appearances, respectively, to compound a miserable season.
They have added heavily this summer though as they seek to improve next season, and Bogdan says they have all been good additions.
“We really would like to push for something to win and obviously finish as high as possible,” he added.
“I think we have a really good team now; the team is really good together. The boys are all good lads and fantastic players, and there's been really good additions to the team as well. Good attacking options, and defensive wise as well.”