The 22-year-old Wigan full-back was in the England rugby league side on Saturday as they lost out to Australia in the Four Nations final at Elland Road.
However, while Tomkins has previously ruled out emulating his older brother Joel's move from league to rugby union with Saracens by signing a pledge not to talk to union clubs for at least the next three years, Barbarians team manager Alan Evans said talks are ongoing about having him play against the Wallabies in the Killik Cup match.
"It's a possibility," he said.
"Over the years we've brought some rugby league players into the Barbarians, some of whom were already on their way into rugby union, people like Sonny Bill Williams and Wendell Sailor, so a precedent has been set.
"I can confirm that we've had talks with Wigan and we hope to resolve it in the next 24 hours."