Milford, who has become somewhat of an outcast at Red Hill in recent times, was said to be the subject of interest from a host of clubs including the Eels as he looks to depart Brisbane.
However Arthur, speaking on SEN 1170 Breakfast, stated that the Eels would not take their pursuit of Milford any further.
“We’re very, very happy with the roster we’ve got," Arthur said on SEN 1170 Breakfast.
“In regards to Anthony, he’s a quality player, but it was only a minor discussion early in the piece.
“I can’t see it going any further.”
With Arthur now turning his back on Milford, it only continues the 'guess-who' over where the two-time Maroons representative will ply his trade in 2022.
There is talk that South Sydney might throw their hat in the ring for his services, with contract talks with star Dane Gagai not playing out as planned.
Milford hasn't been up to scratch in season 2021, only appearing in nine of 17 possible encounters for Kevin Walters' side and his last showing being in round 12 against the Storm.
The Broncos find themselves second from the bottom on the NRL ladder and face the second-placed Penrith this week in what will likely be a painful match for Brisbane.