Both have deals that expire this summer and City have given no indication that they will be offered new contracts.
An Etihad source said: "Palace have been showing an interest in Bacary and Gael for a while, and look like they're ready to make a move.
"They're Premier League position is secured and it was all dependent on if they had that cash as to whether they made a move or not."
The pair both arrived in Manchester via Arsenal and are believed to be happy to move back to London in the summer.
The report suggests Palace could present the French internationals with deals worth £80,000-per-week.