Shawcross says he still hopes to play for the Three Lions.
Asked whether a move might improve his England chances, Shawcross told Sky Sports News HQ: "I don't know, you'd have to move to see.
"I feel like I'm playing well enough to get in the squad, but unfortunately I've not been picked. There are a lot of good centre-halves out there so it's going to be difficult, but all I can do is my stuff on the pitch.
"Hopefully if I play well enough I'll get back in that squad, and if not then I've tried my hardest and hopefully played well."