The 32-year-old former Kangaroo international had another 12 months left on his initial three-year contract with the Giants but will return home on Friday and is expected to join Sydney Roosters. His place was taken by new signing Ukuma Ta'ai for the Giants' 34-6 win over London Broncos on Sunday but Anderson is determined to plug the gap in his squad.
"We're throwing names around at the minute," he said. "What it does is free up fair amount of salary-cap space. We're going through the process of seeing what's the best thing for us. Do we want to bring someone else in like for like or do we want to strengthen other areas?"
He added: "We have a quality squad any way and now have the ability to wait and see if anything falls off the tree either over here or in the NRL."
O'Donnell made just 23 appearances in his first two injury-hit seasons in Super League but made an impressive return in Huddersfield's opening 40-4 win at St Helens 11 days ago.
However, he missed their win over London amid reports that his wife had become homesick and that he had become unhappy over the tightening of tax regulations affecting overseas players.
"It's disappointing for him to be leaving but I fully understand his position and he goes with my best wishes," Anderson said.
Only a week ago the Giants rejected a player exchange deal proposed by Sydney Roosters but Giants managing director Richard Thewlis has confirmed the player had sought and been granted a release with no strings attached.
"Firstly I would say that deep down neither Luke nor the club wanted this outcome to be how things panned out," said Thewlis. "However, the reality is that Luke is financially in a different place now to that envisaged when he joined at the start of the 2011 season.
"The changing regulations in respect of off-shore pensions have caused him significant difficulties - as I am sure it must have for other overseas players in the UK - but fortunately for him an opportunity has arisen back home which will help him going forward."