Wright has been sidelined with a knee injury since December, while Grandison last featured against Swindon last month when he sustained a hip problem.
"Mark Wright has his last injection of the course on today (Tuesday) and once that settles down he should be be joining in," said Turner on Shrewsbury's official website.
"Jermaine Grandison is starting his first straight line running now so he's well on his way to recovery."
The news is less encouraging for top scorer Jon Taylor who may miss Saturday's home match against Stevenage with the groin complaint that ruled him out of last Friday's televised win over Tranmere.
Turner added: "Jon Taylor's groin is keeping him out of training and it will be touch and go whether he's going to be fit for this coming weekend. There's got to be doubts about him."