Well, he wants to play! Lol. Lots of dogs LOVE to play tug. I would actually get a tug toy, and make that the special tug toy. That is the only thing he should be allowed to play tug with, and never a leash.
Does your dog know a solid "drop it" or "give" command? If so, tell him this whenever he tries tugging with the leash. Never give in to his play drive if you want to stop him from tugging on the leash. But, I recommend TO play tug alot with the special tug toy. Soon he will learn which toy and when it is the proper time to play tug.
If he does not yet know "drop it" or "give", you have some work ahead of you! The "give" command is a very important one. All my dogs learn this. If they have something I CANNOT let them have, it is so much easier to just ask them to drop it rather than fight with them to get it out of their mouths.
To teach "drop it" or "give" be prepared with REALLY yummy treats. Chicken, hot dogs, cheese, or whatever REALLY motivates your dog should be used as treats. If you have a toy(ball, stuffy, frisbee, etc), you can start teaching with the toy. (*Note-it is best not to ever play tug until your dog is solid on the "give" command.) If he ever willingly lets you have the toy(say, to throw it) say "give" and give him the REALLY yummy treat! If ever the dog does not comply to the "give" command, do not scold or yell. You have to wait. Yes, wait. Sometimes this takes a very long time. You wait until he gives it up willingly. Or, you could also tempt him to give you the toy by offering a treat. If this works, give him the treat and end there.