Egypt international Salah has been linked with a move to the Premier League for some time, with Liverpool reportedly negotiating with his club throughout the ongoing transfer window with a view to bringing him to Anfield.
However, Chelsea revealed on Thursday that they had agreed a fee with Basel for the 21-year-old as Juan Mata edges closer to his switch to Manchester United.
And Mourinho said that a conversation with Salah has left him "confident" that the winger is on his way to Stamford Bridge, even though Liverpool boss Brendan Rodgers had told TalkSPORT earlier on Friday that he had not given up hope of signing the player.
"We have an agreement and that only goes forward when there is an agreement with the player," said the Chelsea manager.
"We know he wants to come, he told me personally but it is now terms and medical he has to pass."
Mourinho went on to say that Chelsea had to move quickly to secure a replacement for Mata, who has been given permission to undergo a medical at United.
"It was a surprise for us that Juan was leaving," added the Portuguese.
"We were not prepared to make a bid to replace Juan in the squad. Everything happened very, very fast.
"We had to work on that and see what options could be good options. We decided to go for Salah and started from zero. We knew nothing.
"The first step was an agreement with the club, as we made official we reached agreement with Basel. That is done, subject to the medical and subject to the player's desire to join us or not.
"Now we know he wants (to sign) and now he is very happy to come but we have to finalise. We have to travel to do his medical in Switzerland."
Chelsea have also been linked with Saint-Etienne defender Kurt Zouma in January, and Mourinho revealed that dialogue is open with the 19-year-old.
"Chelsea thinks about the future ... and when we have permission, as we did in this case, we contact the player," he added.
