Winger Taylor, who has been in inspired form over the last two months, was forced off at half-time in last weekend's 2-1 defeat at home to Sheffield United nursing a groin injury, while fellow six-goal striker Morgan missed the game altogether due to an ankle problem.
Manager Graham Turner told Town's official website: "Jon's missed training all week so he's a big doubt. Marvin Morgan missed last weekend's match, he's trained so there's a possibility he will be fit."
Shrews are boosted by this week's arrival of striker Chris Porter on a one-month loan deal from Sheffield United and he will be in line to make his debut at Prenton Park.
Long-term absentees Jermaine Grandison (hip) and Mark Wright (knee) continue to miss out.