Brown, who joined Sunderland from Manchester United, earlier this month has yet to figure for his new club this pre-season as he recovers from a minor injury.
The 31-year-old is due to make his debut against Kilmarnock on Wednesday and he is hoping to prove his fitness ahead of the big kick-off against Liverpool on 13 August.
"I get a game in tomorrow it will be my first game and I am looking forward to it," Brown told Sky Sports News. "The more games I play now the better I will become.
Asked if he will fit for the opening day trip to Anfield, Brown added: "Yeah I should be. If I get in the next few games of pre-season I should be ready for the 13th and Liverpool."