Mourinho sought the advice of his defensive pair before agreeing to bring the out-of-sorts Manchester United forward to Stamford Bridge, and they told him he was still an attacker to be feared.
Both came up against Falcao when Chelsea beat United 1-0 at Stamford Bridge in April, and although the former Atletico Madrid star did not score, he hit the post in the second half and Terry and Cahill found him hard to handle.
Mourinho said: “I watched our game against Manchester United a few times.
“I spoke with John and Cahill a lot about him and we think the bright movement is there, the movement to get freedom in the box to score goals is there.
“Our players had difficulty to control him and we feel the potential is there. Let’s see if he can improve his confidence, his happiness.”
He surprised many when he signed Falcao on loan from Monaco this summer after the 29-year-old failed to impress at United last season.
The Colombia striker scored just four goals for United and was dropped to the reserves by manager Louis van Gaal.
It was a very different record when he was at Atletico, where he scored 52 goals in 68 La Liga games between 2011 and 2013.??He also scored a hat-trick against Chelsea in the 2012 Uefa Super Cup final, confirming his place as one of Europe’s top strikers.
But he has not been the same player since suffering a serious knee injury while he was at Monaco in January 2014.
Mourinho, however, who already regarded Falcao highly from his spell as manager at Real Madrid, is convinced he can help the forward re-find his attacking flair and said he had no hesitation in giving him a second chance in English football.
He doesn’t see Falcao as a back-up to Diego Costa, who made such an impact on the Premier League after joining Chelsea last summer.
“He can be second, first or third [choice],” Mourinho said: “He knows, Diego knows and [Lo??c] Remy knows that. It is open competition between the three of them. That’s our objective, that???s why we want three strikers ready and important.
“If we want, we can play with Costa and him together – it is something they did before when they were in Atletico. Can he be the Falcao of Atletico? We believe so.
“Every team has their style of play and every manager has their way of football. If Mr Van Gaal didn???t play him more it???s because he had his ideas and we have to respect that.”
Falcao will join his new team-mates on Tuesday on their pre-season tour of North America, having been given extended time off after playing in the Copa America, but will not play against New York Red Bulls on Thursday nor Paris Saint-Germain on Saturday.
He said: “We are not expecting him to join us Tuesday and then play on Saturday and score a hat-trick. But he has to be ready for the first league game. Maybe not the Community Shield [against Arsenal on 2 August]. But after two and a half weeks of training, he must be ready.”
Mourinho added: “He is not happy that in England people think he is not as good as he is and his motivation is there. He lost money to come to us; he didn???t want to listen to other offers.”