i would be getting worried and would start working on this straight away before it becomes a big problem.
if he is trying to push between you two tell him off and push him away. get him off the couch if he is sitting between you etc etc. don't let him show any "jealousy" towards you.
also if it is possible take turns in feeding / walking, or go for a walk together in the afternoon / night whenever suits you. This is more of a taking on the role of him basically seeing your girlfriend as HIS girlfriend (sounds silly but it was the easiest way i could think to explain it) also it would be great if both of you were able to do some training with him so he has respect for both of you
"In order to really enjoy a dog, one doesn't merely try to train him to be semihuman. The point of it is to open oneself to the possibility of becoming partly a dog." - Edward Hoagland