Chris infamously beat Rihanna up the night before the Grammy Awards back in 2009.
The source said: "Jay was absolutely disgusted by what Chris did to Rihanna. Jay doesn't understand how a man could ever lay hands on a woman; it just goes against who he is and what he's about. Chris is absolutely dead to Jay, he wants nothing to do with him ever.
"Now that Rihanna is hooking up with Chris and recording songs with him, Jay is deeply disappointed in her actions. He can't fathom why Rihanna is doing the things she is doing. He understands the need for forgiveness, but he is adamant that Rihanna shouldn't forget what Chris did to her."
And the seemingly very well-informed source went on to suggest that Jay-Z is concerned about the message Ri-Ri is sending to her young female fans.
The mole continued: "Jay has told Rihanna he will never give his blessing for what she is doing with Chris. He has told her this isn't going to end well, it never does. In Jay's opinion, Chris has rage issues that he doesn't think have been dealt with."
And Ri-Ri has also been fending off criticism from fans on Twitter over the move.
A fan going under the name @JuhReeV had tweeted: "I gotta admit, I lost a lot of respect for @rihanna...Makin a song w/the dude that beat your face off is not a good look."
And Ri-Ri hit back at her and other fans by responding: "@JuhReeV neither is your avi #clapback" (avi is short for avatar) and "U Mad? #No1Currrrr" (search us).