The Daily Mail says Abramovich has held two meetings with the player's brother and agent, Roberto de Assis - the last summit being on the weekend in London.
The Russian billionaire spent the weekend entertaining Assis, flying him in on his private jet and putting him up at the exclusive Lanesborough Hotel in Mayfair. Abramovich held the second meeting with Assis at his Knightsbridge house on Saturday morning and is understood to have put an offer to him that would make the Brazil star the highest paid player in Europe.
It will, however, dwarf the £130,000-a-week deal recently agreed with captain John Terry.
Luring Ronaldinho from the Nou Camp is not going to be easy, and not just because the summer transfer window closes this Friday.
There is the buy-out clause in the contract Ronaldinho signed at Barcelona in September 2005 which runs until 2010. It is a staggering £85million.
But Abramovich is desperate to see his Chelsea side play with more flair and adventure, not least after seeing them stutter to a 1-0 win against Portsmouth on Saturday, and would consider it money well spent for the 27-year-old, who has twice been named World Player of the Year.