Reds boss Brendan Rodgers is desperate to add some new firepower to his misfiring squad this summer and is keen on luring the Colombian flop to Anfield.
But he will have to go head-to-head with former mentor Jose Mourinho for the Monaco hitman.
Mourinho hinted yesterday that a deal is already in the bag for Falcao, who endured a miserable season on-loan at Manchester United.
He said: “If I can help Falcao reach his level again, I will do it.
“It hurts me that people in England think that the real Falcao is the one we saw at Manchester United.”
But reports in France claim Falcao might prefer to join the Reds instead, despite the fact they are in the Europa League next season.
While on loan at Old Trafford he cost United £16m in wages and fees but was a huge let down after scoring just four goals in 29 appearances.
He struggled to hold down a place in Louis van Gaal’s side and was even reduced to tears when the United boss made him turn out for the club’s under-21 team.
United have rejected the chance to sign him on a permanent deal for £42m – but this hasn’t stopped Falcao from finding himself in demand.
The Blues are in talks with Monaco about a deal, but one stumbling block is likely to be Falcao’s £275,000-a-week wages, which are way outside the club’s pay structure.
Chelsea can offer Falcao Champions League football but he would have to accept a wage cut to seal a move to Stamford Bridge.
Mourinho insists he will not ship out fellow Colombian Juan Cuadrado to make room for Falcao.
The winger made just four Premier League starts following his £26m January move from Fiorentina.
But despite interest from Roma and Inter Milan, Mourinho said: “He is going nowhere this summer.”