Not sure if anyone has seen but EA have launched 2 games on the Ubuntu Software Center, it's not much but my guess is they're just testing the waters looking to see if there is any potential. Here's the article: OMG Ubuntu
As the article states "It’s now up to us, as users, to prove to EA that gaming on Ubuntu is worth pursuing" and as a result I have created a thread on EA's forum letting them know how many games I own on Origin and that I am infact an Ubuntu user.

If you own any EA games or would like to see more EA games on Ubuntu please do swing by the thread and leave comment, here's the link: EA Forum
I did leave this as a reply in another thread but only realised after I posted it that it wasn't in the Gaming & Leisure section of the Forum.