If you are successful in defeating the enemy and they reach the requirements below, they can ask for peace by themselves. If you decline their offer, your turn to ask for new negotiations has to wait for 50 days.
Keep in mind that these requirements may vary after each update as I'm constantly tweaking them. Nevertheless they should always be similar.

• They need to have at least 20% capitulation progress
  
• You are not allowed to have some territory of yours occupied
  
• 90 days since you started the war
  
• The conscription law must be "Limited Conscription" with 10000 manpower left OR "Extensive Conscription" or higher
  
• The economy law has to be at least "Partial Mobilization"
  
• The option has to be enabled in the setup event