During an interview with Polygon, Lars Gustavsson from DICE noted that the company is quite keen on getting into development for Linux OS and that it would only take a single big title for platform to become mainstream.
In the same interview, Gustavsson noted that Valve's Steam Machines are quite a good move and will definitely improve the situation in the Linux OS gaming. Although it did not go into details regarding DICE's involvement with Linux OS and did not specify any titles that might be ported to Linux, the best guess is that DICE is definitely aiming to bring its Frostbite engine to Linux as it would not want to pass that great opportunity.
In any case, if anyone could bring Linux gaming to mainstream, it is certainly Valve.
Source:
Polygon.com.