Jeffers has been sidelined since sustaining the problem in the 1-0 defeat to Gillingham last month and boss Leam Richardson revealed the former Everton and Arsenal man is champing at the bit.
"It would be a huge boost to have him available," Richardson told Stanley's official website. "He has trained a bit this week and we continue to monitor him, but whether he is match fit we will see.
"It's a constant conversation we are having and hopefully we can look at him for the weekend and if not that then fingers crossed he'll be available for Oxford."
Fellow hamstring victim Nicky Hunt made an ahead-of-schedule return to Accrington's matchday squad for last Friday's 2-0 win over Morecambe and the defender is expected to be involved once more.
The Reds are unbeaten in their past four games and, after just one defeat in seven, head into the penultimate game of the season three points above the relegation zone.
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