Dowson delivers injury update ahead of Saints' clash with Sale Sharks
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Odendaal has been battling injury issues since arriving at cinch Stadium at Franklin's Gardens during the summer.
The South African centre, who joined from Japanese side Toshiba Brave Lupus Tokyo, picked up a shoulder problem before moving to Saints and then was hit with a hamstring injury in training.
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Hide AdBut he has been on the recovery trail and he is now getting closer to wearing the black, green and gold for the first time.
"He's closer," Dowson said. "He's in the mixer. He's done a couple of weeks' training now."
Saints are also hopeful of a return to action for Ollie Sleightholme, who suffered a hip problem during the win against Toulon earlier this month.
"Hopefully Ollie Sleightholme pulls through this week with his hip pointer so there's hope for Ollie," Dowson said.
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Hide AdHowever, George Hendy (knee) and Tom Seabrook (ankle), who were both also injured during the win against Toulon, face longer spells on the sidelines.
"They're both on crutches so they're going to be a long period of time out," Dowson said. "They will be out for an extended period of time."
Alex Waller suffered a neck injury in the victory at Glasgow Warriors, but Dowson said: "Alex Waller is good so he'll be there or thereabouts."
Lewis Ludlam is another player who has been sidelined as he sustained a high ankle sprain in the success against Harlequins.
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Hide Ad"Lewis Ludlam is going through the return to fitness so he's a little way off just yet," Dowson said. "But he's working hard at it because he's desperate to get back."
James Ramm is a long-term absentee with a knee injury, while Tom James is set to serve the second match of his three-game ban this weekend.