Tomkins played for England's rugby league team against the Kangaroos on Saturday.
The 22-year-old Tomkins recently pledged his future to rugby league, ruling out the prospect of following older brother Joel to Saracens by signing a pledge not to talk to rugby union clubs for at least the next three years.
But Barbarians team manager Alan Evans said talks are under way with Wigan for Tomkins to make a one-off appearance in the Killik Cup match against Australia.
"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."
Tomkins, one of rugby league's brightest prospects, was in the England team that lost 30-8 to Australia in last night's Gillette Four Nations final at Elland Road.
His rugby league commitments are now over until the start of pre-season training with his club and he is said to be considering the offer to run out at Twickenham.
The Barbarians, coached by Graham Henry and Steven Hansen, have already announced a provisional star-studded 22-man squad drawn from 11 different countries including the likes of Mauro Bergamasco and Victor Matfield.
The squad is expected to be finalised on Monday and will assemble in London on Tuesday.
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