PSG believe that Mbappe has already reached a verbal agreement with Real Madrid for a free transfer. PSG are at the point of no return about Mbappe's future now seemingly. They waited for an answer from Mbappe about what he is going to do with his future and there has been no answer. From now on PSG have decided to do the sensible thing they should do. They are open to hear about any kind of formula from other teams for Mbappe from now on. The main goal is to not send him for free now.
However I don't believe Real Madrid will make an offer this summer as long as there is none from others. PSG had better hope for other rich teams to intervene and fire up the race for Mbappe.
Mbappe may have reached a verbal agreement with Real Madrid and upon reaching a verbal agreement, asked Real Madrid for some time so that he could be released and then join Real Madrid, in which case Real Madrid may have accepted Mbappe's terms and given Mbappe one more season. Since Mbappé is very unlikely to stay at PSG, PSG should plan without Mbappé. And PSG may be planning how to prevent Mbappe from changing clubs as a free agent. In other cases where the club has full rights but in Mbappe's case it is completely different Mbappe's behavior seems like the club is responsible to him and not to the club. Maybe he will join Real Madrid as a free agent member as planned by Real Madrid. PSG may not be able to block Mbappe from changing clubs as a free agent.