"Yes, we have made an offer to Ronaldinho but it is still in the early stage," Venkateshwara Rao, joint managing director of Indian poultry giant Venky's, told Reuters.
"Similarly, we have made an effort to get Beckham on loan but again, nothing has come out of it so far."
Beckham, who has asked Los Angeles Galaxy if he can make an off-season loan move, has been linked with Tottenham Hotspur although other Premier League clubs have expressed an interest.
Rovers manager Steve Kean, who Rao said could be offered a longer deal after being put in charge until the end of the season, said he would welcome the signing of Ronaldinho.
"I know there has been contact made by the owners to representatives of Ronaldinho but I don't know how far down the line it is and whether it will actually happen," Kean, who stepped up from assistant manager after Sam Allardyce was fired last month, told reporters.
"If any Premier League manager was asked if they wanted to sign someone who has been World Player of the Year twice they would be interested.
"Everyone should look at it as a positive, it has been a long time since we have been able to do that."
Rao declined to reveal how much the club was offering Ronaldinho to lure him to Ewood Park after the former world player of the year left AC Milan's Dubai training base to return to Brazil and find a new club.
However, it would be a significant coup for the new owners of Rovers if they could attract a player who wowed crowds with his brilliance while at Barcelona from 2003 to 2008 and who helped Brazil to World Cup glory in 2002.
AC Milan owner Silvio Berlusconi said the club was sorry to see the 30-year-old Brazilian go.
"I'm sorry he went away, he is the greatest player in the world in terms of speed of thought and execution. But it was his choice to return to Brazil," Berlusconi told reporters on a visit to a Milan training session in Rome.
Ronaldinho and his brother-agent are now talking to Brazilian clubs including Gremio, Flamengo and Corinthians about a January move.
