Blues boss Carlo Ancelotti has previously stated there will be no transfer activity next month but that looks set to change following just one win in the last six games.
Abramovich is now ready to splash the cash and is keen to bring Aguero and Leko to the club, while Everton's Jack Rodwell, Ajax's Uruguay forward Luis Suarez and Roma's World Cup winner Daniele De Rossi are also on his list of possible targets.
"Abramovich has drawn up a list of options for the New Year," a source close to the club has been quoted as saying in the Sun. "Atletico are asking silly money. If they don't get real Roman will switch to Suarez and try to do a deal with Ajax instead.
"It's not just strikers, though. Jerko is the one they are looking at to come in as a defensive midfielder, although De Rossi and Rodwell are also on the radar.
"So it should be a busy time because the desire is there, the money is there, the options are there."