Blackburn beat Arsenal 1-0 in the last round, and the Lancashire outfit will travel to The Den on Sunday to face Millwall in an FA Cup quarter-final.
Dann told the Daily Mail: "A lot of people will say we've got one of the more fortunate ties this round and they're probably right. We won't have a better chance in God knows how long to get to the semi-finals.
"But Millwall will be thinking exactly the same. They would rather play us than United, City, Chelsea, Everton or Wigan. You don't want to count your chickens."
Scott Dann moved from Birmingham City to Blackburn Rovers in 2011 for £6m.