Таблица items, таблица users, таблица user_items
create table user_items (
user_id int,
item_id int,
ownership enum('changed','confirmed')
);
-- Let user 1 have item 100
insert into user_items values (1, 100, 'confirmed');
select * from user_items;
-- user 1 offer his item 100 to user 2
update user_items set user_id = 2, ownership = 'changed' where item_id = 100 and user_id = 1 and ownership = 'confirmed';
select * from user_items;
-- user 2 confirm ownership
update user_items set ownership = 'confirmed' where item_id = 100 and user_id = 2 and ownership = 'changed';
select * from user_items;
MySQL fiddle
Можно добавить поля дата передачи и предидущий собственник