The professional basketball player left their house last Wednesday and returned this past Tuesday, the celebrity news website said.
Although the couple are working on their relationship, Odom remains undecided about how to deal with his substance abuse problem, TMZ said.
However, Odom is "open to reason and listening to the people who love him the most," which is a big difference from a week ago when he walked out of an attempted intervention, the report said.
Kardashian married Odom in 2009 after a whirlwind romance.
Celebrity Breakups and divorces of 2014 [PHOTOS]