Smith has told Super League leaders St Helens he would rather train than play for Eagles who are fourth from bottom in the Championship.
Smith, who turns 31 next week, has made only four substitute appearances for Saints so far this year after losing his half-back spot to Danny Richardson, along with three starts as a stop-gap replacement for hooker James Roby.
He made one appearance for Sheffield on dual-registration against Toulouse on July 1, but has turned down the chance of more rugby with the part-time tier-two club.
“He’s just going to keep on training,” said Saints coach Justin Holbrook.
“He just wants to keep his conditioning up.
“We had some lengthy chats about what he’d prefer to do. He obviously had one game there and he thought it was best for himself to just train harder all week. He’d rather continue with his conditioning and I’m okay with that.”
Smith, who returned to his hometown club after helping Wigan win the Grand Final in 2016, will remain on standby in case of injury, but Holbrook has used only 22 players so far this year and has no plans to rest anyone, despite challenging on both fronts.
Catalans Dragons, Widnes and Leigh all made attempts to take Smith on loan earlier in the year and the one-time international continues to be linked with a move to the French club for next season.