The Blues boss says he is "hurt" that supporters of the Premier League think the "real" Falcao is the Colombian striker seen floundering on loan at Old Trafford, where he scored four goals in 29 appearances for United.
Chelsea are understood to be in discussions over a move for the Monaco forward, who is currently on international duty at the Copa America.
However, any move could hinge on the Blues negotiating a significant reduction in his £265,000 a week wages, which are outside Chelsea's salary structure.
Mourinho told DirecTV Sports on Wednesday night: "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."
Chelsea have a striker vacancy after Didier Drogba left on a free transfer.
Falcao's first European club was Porto, where Portuguese Mourinho came to prominence.
Source : PA
Source: PA