I suggest we play tennis,.......................?

I suggest we play tennis,.......................?

The answer is

I suggest we play football , shall we?

Would you please tell me where you got this answer from, as I searched on the net for such sentences and I couldn't find appropriate answers. Also I'm a member in one of the English forums run by native speakers and they find this answer as "odd" so please tell me which reference book you have got this answer from. Thanks in advance. By the way I'm not a student. I'm a teacher .And I want to apologize that I have written my question here because I haven't noticed the title of this section that it is for students not for teachers. Getting back to my question, I agree with you that the sentence implies suggestion and this is the way I answered it but when I wrote it on the forum I mentioned to make sure of my answer. Their reply for "shall we" was that seemed odd.