The 25-year-old Londoner has done well on Tyneside since his £6.5m move from Chelsea last summer despite the knee injury which kept him out of four games last month.
Graeme Souness, the man who persuaded him to head for St James' Park, repeatedly championed his cause, but Parker is yet to be included in a national squad as a Newcastle player and still has only two full caps to his name.
With central defender Ledley King having been used in midfield with mixed results, there is a growing campaign for Sven Goran Eriksson to take a holding midfielder to Germany and Roeder is convinced Parker could do the job.
"I think Scott has a chance of the World Cup," Roeder said. "He was really unlucky in terms of what happened to him at Chelsea.
"I remember in his last season at Charlton when I was manager at West Ham, he was their whole midfield. It did not surprise me Chelsea forked out £10million for him after that.
"Scott has come up to Newcastle and you can tell already the fans love him," Roeder added. "He has that devilment in him that the supporters associate with themselves - the will to win.
"It is great to have in your team because it drives the other players. When they see that, they want some of it.
"We need good fortune to keep people like Scott and Kieron [Dyer] fit. This is a small squad, but a small squad of quality.
"Fortune is out of our hands, but the club deserves to keep its best players fit."
Meanwhile, the hunt for Souness's replacement continues as the Newcastle chairman, Freddy Shepherd, conducts an assessment of the potential contenders.
The former Bayern Munich manager, Ottmar Hitzfeld, is receiving some popular support, although Martin O'Neill remains the overwhelming popular favourite, with the former Chelsea manager Claudio Ranieri's odds having shortened significantly.