The Lions are aware that Rovers chief Graeme Souness is a fan of the Republic of Ireland midfielder, and it had been suggested the Scot was plotting a summer raid.
Millwall chief Theo Paphitis has dismissed reports which suggested Rovers had lodged a bid, but did not rule out the possibility of Souness contacting them at some point in the future.
"There has been talk of that for over two years," Paphitis said. "We have had no offer from Graeme Souness."
Lions boss Mark McGhee does not expect any contact unless Rovers sell Reid`s international team-mate Duff.
"Souness has made it very clear he admires Reid as a player," said McGhee. "I would imagine Blackburn are waiting to see what happens with Damien Duff.
"If they sell him, one of the players I am sure they would be interested in signing would be Reid."
