The Roosters parted company with coach Ricky Stuart on Monday and Anderson has been linked with the vacant position.
But Anderson insists he is committed to his Challenge Cup winning side, who face relegation-threatened Wakefield on Friday.
"There has been no contact with the Roosters at all. I can't control the speculation so I'm not going to worry about it," he said.
"My aim is to back these boys up this Friday for the league leadership."
Prior to his role at St Helens, where he succeeded the sacked Ian Millward midway through last season, Anderson coached the New Zealand Warriors to an NRL Grand Final against the Roosters in 2002, before coaching the Kiwi national side.
This year has been a huge success for the Saints under Anderson. They are four points clear at the top of the Super League and crushed Huddersfield Giants in the Challenge Cup final. Anderson is contracted to the club until the end of next season.
He added: "I don't know when but I am going to go home. I have never tried to hide that fact.
"Ricky is surprisingly not coaching and the next day I'm coaching in the final the other side of the world. I make an easy media target."
"He has said nothing about his family not being happy here. He's doing a great job, we want him to stay and I've nothing to indicate that he won't."
Stuart had been at the helm at the Roosters for five years during which he steered them to three successive Grand Finals. This year though they have won just eight matches and he has been told that this weekend's game will be his last in charge at the club.
Roosters chairman Nick Politis said: "We'll look at who's available and who will do the best job for the club."
On a more positive note, St Helens' injury-hit second rower Mike Bennett has signed a new two-year contract with the club.
Bennett, 26, has made just four appearances this season because of two shoulder injuries but is set to make his comeback in Friday's Super League match against Wakefield.
He said: "I am very pleased to be staying with Saints. I have been unlucky with injuries this year and would like to thank the club for their support and patience.
"I am determined to have a strong finish to this season and get back into the first-choice 17."