The Spanish giants are desperate to keep Messi but have been stunned by news Abramovich wants the Argentine so badly.
And with almost £100m on the table, the Barca hierarchy are split on the decision to sell.
A source close to the proposed deal said: "Roman is convinced Messi could change the whole face of Chelsea and is willing to spend what it takes to get him.
"He has always wanted that type of player. Under Jose Mourinho he accepted the football because it was bringing in the trophies but he got bored. Grant wants to change things but has explained it takes time and a lot of money to alter the style.
"Now is the time for Roman to finance that change. Chelsea are attractive because of the wages on offer and they are in the Champions League Final."