The Daily Star says the Colombian international, 27, is hoping to push through a move away from the big spending French club only four months since his £40m arrival from Atletico Madrid.
Real Madrid boss Carlo Ancelotti is also interested in bringing Falcao back to La Liga and according to reports in Spain, the striker has asked to leave Monaco on-loan once the transfer window re-opens.
Chelsea will look to secure a loan deal to bring Falcao to Stamford Bridge in the upcoming January transfer window.
Manchester United also hold an interest in Falcao, however David Moyes has made adding to his midfield his main priority in the winter window leaving Madrid as Chelsea's main competition for his signature.
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