Sturridge was given a rare start as the Reds drew 1-1 with the Magpies on Sunday, with the England international struggling to impress at St. James' Park.
Speaking on BBC Radio 5 Live (h/t James Cambridge of the Daily Express), Wright said the 28-year-old needs a fresh start.
"I think Newcastle would be the ideal club for Daniel Sturridge," he said. "The fans would take to him there."
Former Liverpool manager Graeme Souness thinks Sturridge will now spend an extended period on the bench after his poor showing against Newcastle.
In his role as a pundit for Sky Sports (h/t Stuart Ballard of the Daily Express), he said:
"He was laboured, a yard off the pace, I don't think he can train properly, and that's why he gets injury after injury.
"I was watching him last year, and his warm-up was like 30 per cent. Then he is expected to sprint when the game starts.
"It might be another month, six weeks before Klopp plays him again.
"[Jurgen] Klopp sacrificed the work rate of Firmino for a bit of magic from Sturridge, but he didn't have it, he laboured today."
The former Chelsea man started just seven games in the Premier League last term, scoring three goals, according to WhoScored.com. Sturridge has remained rooted to the bench, with manager Jurgen Klopp withholding his faith in the player.
Mundo Deportivo (h/t TalkSport) reported the 21-year-old's stock has risen, with top teams eyeing up his talent for future transfer windows.
The Germany international has grown in stature, and Squawka highlighted his recent run of form:
Squawka Football @Squawka
Timo Werner for club and country in 2016/17: 38 games 🏃 24 goals ⚽️ 7 assists 🅰️ A superb talent. ⭐️ https://t.co/4scD5EAPZ02017-7-2 21:42:34
Werner could be viewed as a long-term replacement for Sturridge if he is purchased by Klopp, with the young German offering world-class potential.
Sturridge's time at Anfield does appear to be coming to an end, and the striker should analyse advice to find a new team.
The England man has lost the confidence he had when partnering Luis Suarez for Liverpool, and he remains a shadow of the player he once was.