Mourinho, visibly touched by Aleksandrovic's story, agreed that the photograph would be arranged and Tottenham have posted it on Twitter.
Aleksandrovic had initially missed his chance to make personal contact with Mourinho at a media gathering on Zoom before Tottenham's Europa League qualifier with Shkendija on Thursday.
Word made its way back to Tottenham's media team and Mourinho was brought back into the room on Wednesday.
Aleksandrovic said: "First, greetings to you from him, but he is now in heaven. One of the occasions when he was very sick he told me if I ever have the opportunity to see you, to ask for a picture with you because he always raised me like you when you are the head coach of any team, psychologically winning or losing -- he has massive respect for you.
"If you allow me a picture of you I will frame it and put it in his eternal resting place. If the match goes good for you and your team will you allow me to do that?"
A humbled Mourinho replied: "Thank you so much. The picture has nothing to do with the result.
"The picture is done, let's do it. If you can meet us before the game, or maybe in the hotel is easier. If it's after the game, it's after the game. It's nothing to do with results.
"My pleasure to do the picture with you. And my honour to your father and respect that he feels so strong about me. I don't deserve that."