Van der Sar announced his decision to retire last week, and United boss Sir Alex Ferguson has been linked with a host of goalkeepers to buy during the summer, but the Polish stopper thinks he has what it takes to replace the 40-year-old.
He told uefa.com: "I have already proved something to myself by playing over 60 matches for United, but I would also like to prove to others that I can be Edwin van der Sar's successor.
"My goal remains the same: to be No. 1. It is one of my two big football dreams. The second, of course, is to play for Poland at Uefa Euro 2012."
The former West Brom man faces stiff competiton from new signing Anders Lindegaard, who debuted in the FA Cup victory over Southampton at the weekend, and the Pole admitted that he hopes to play more to ensure that he plays for his country when they host the European championships.
"I think that my chances of playing at Euro 2012 will only be decided just before the tournament," he said.
"Of course, I want to play more than I do right now. This is a very important time in my career."