How to deal with Toxic Employee seeking new job

My organization was bought out by another company two years ago. One long time employee, who was recently transitioned to a position he did not want, has been loudly proclaiming his extreme discontent and criticism of the company to everyone who will listen. He brazenly tells us all about every interview he goes on – even informing his own manager of the exact reason he will be out. He is spreading malcontent like a toxic virus… What can be done? Can this be construed as creating a hostile work environment?

For additional context, our organization has had a few rounds of layoffs recently and this person does have skills we need. There will be an impact on the morale of the remaining employees if we fire him… Thanks!