Shayk recently walked the red carpet at the Met Gala alone, once again fuelling rumours that her relationship with Cooper was struggling.
Cooper and Shayk have been together since April 2015 but E! News reports they are now considering whether they should break up.
"Things get a little bit better but then they find themselves back in the same place of questioning whether being a couple is what's best," a source told E! News.
"They want to stay together for their daughter, but neither of them are very happy.
"They've spent time apart to test the waters and see if they are better off," the source added.
"They have a lot invested and it's very difficult to completely walk away from. They are trying out different arrangements and trying to find their way.
"They love their little girl dearly and that's not going to change no matter what."