At the start of the season, Pope was on the bench for the Clarets, but a long-term injury to Tom Heaton has resulted in the 25-year-old making 27 outings in the Premier League.
Pope is an outsider to make Gareth Southgate's World Cup squad, but the former Charlton Athletic stopper has claimed that it is "every man for himself" until the final 23-man group is named.
At a press conference, Pope told reporters: "If I wasn't in this squad I would be an outsider for the World Cup at most. I have got to prove myself at this level.
"I've come here to enjoy it and show what I am about. In football, you have to be hungry and I am happy to be here.
"There has got to be one number one. Come the World Cup, there will be one goalkeeper who has that slot. There are eight games left of the Premier League season and it is every man for himself."
England face the Netherlands on Friday, before hosting Italy at Wembley Stadium on March 27.