Huw Marshall registered WayneRooney.com and WayneRooney.co.uk in April 2002, when the striker was just 16.
The case has been taken to the United Nations’ World Intellectual Property Organisation in Geneva, Switzerland.
Mr Marshall, who is in Welsh-language drama Tipyn o Stad, said it was with solicitors and he could not comment.
Rooney, 20, has become one of football’s biggest stars with Manchester United and England in the past few years.
His profile soared in October 2002 when he hit a spectacular last-minute winner for Everton against Arsenal to become at the time the Premiership’s youngest goal-scorer.
But six months before that the two domains in his name had already been registered.
Anyone trying to log on to WayneRooney.com or WayneRooney.co.uk at present is told that the sites are “coming soon”.
Mr Marshall, who is originally from Wrexham – just across the Welsh border from Rooney’s home city of Liverpool – plays the head of a troublesome family in Tipyn o Stad, a series on the Welsh fourth channel S4C.
The actor told BBC News he had been advised not to comment.