Castleford are taking legal action after Solomona "retired" from rugby league, only to be registered by Sale.
The RFU say they respect RFL concerns regarding the "sanctity of contracts" but do not have jurisdiction to act.
"The employment status with a club in a different sport is a matter between that club and the player," a RFU spokesman told BBC Sport.
On Wednesday, Rugby Football League chief executive Nigel Wood said he was worried about the "implications for the game" after 23-year-old Solomona was added to Sale's European Champions Cup squad.
Despite the registration, the Samoa rugby league international's move to rugby union is yet to be confirmed by the Sharks.
Solomona, who set a new Super League try-scoring record in 2016 by crossing 40 times, failed to report for pre-season duty with Castleford in November, prompting the club to take legal action.
Premiership Rugby have been contacted by the BBC for comment, but are yet to respond.
The Rugby Football Union will not stop Sale signing Denny Solomona, despite a cross-code legal battle for the player.