Brown is available on a free transfer due to a release clause in his contract following Rovers' relegation from the Championship.
Should he leave, the 29-year-old will follow Mark Duffy, who has joined Birmingham, as the second player to activate such a clause in his deal.
"I don't think it's any secret that Blackburn are interested in Browny," said Dickov.
"I've been in regular contact with him and he's been very up front from the start.
"I think a big part of Chris would want to stay but the lure of Championship football is too much for him.
"We all would love Browny to stay but I don't think the fans and staff at the club who saw him last season would begrudge him the move, and a decent move at this stage of his career.
"He was outstanding for us last season. We wish him all the best - if it does happen."
Brown joined Doncaster on a free transfer from Preston three years ago and made 97 appearances for Rovers, scoring 23 goals.