The Frenchman will be offered a deal which takes his weekly wage from around £20k a week to £30k after impressing on his appearances this season.
Sources inside the club have told ClaretandHugh: “Morgan is one of those we want to keep and we are working on a deal to put in front of him.
“He certainly hasn’t let himself down and is proving to be a player who can make his presence felt.
“We have clinched the signatures of Winston Reid, Mark Noble and James Tomkins which has made it a great late season.
“It’s important that we clinch as many as we can among the current squad before we move the strengthening in the summer market.”