The abbey has only been open for private prayer and public worship, but church members are hoping they will be able to open the premises to visitors in November.
It comes after the abbey received nearly £100,000 from the government's Culture Recovery Fund.
Rev Dr Thomas Atfield said the funding will be used to improve accessibility.
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Mr Atfield, vicar of Holy Cross Parish including Shrewsbury Abbey and St Peter's Church in Monkmoor, said: "We'd very much like to open for tourism next month subject to government conditions.
"One of our biggest problems is that we've had a five-month battle with pigeons, which we've just overcome.
"We've been making the abbey safe and attractive and spent the last week deep cleaning – it looks fantastic and it's no exaggeration to say it's the best its looked in years.
"We're hoping over the next few weeks to bring back some of our amazing volunteers, guides and stewards to offer them training and safeguarding in working with the public in a Covid-secure world."
Mr Atfield added: "We are delighted to receive the grant funding, which will go towards access to the Abbey.
"We're putting accessible doors and pathways in and we're spending £10,000 of that money on new interpretive and historical signage inside.
"The current doors to the abbey were put on in the 1970s and 80s and aren't access-friendly to a large number of people, including wheelchair users and anyone with mobility issues.
"In order for people to enjoy our space they need to be able to access it, and this will form part of a £483,000 project we'll be seeing through in the next few years to make the abbey as welcoming and accessible as we possibly can, allowing us to host as many events, concerts, exhibitions and community groups."