“The deadline is going to be tight, it’s going to be right up to the line.”
Mr Tolkien has applied for planning permission application to put the statue in the park.
Council leisure boss Martin Mullaney said: “We want pilgrims to touch the statue. Cofton Park will become a site of pilgrimage together with the Birmingham Oratory and Oscott College.
“It could become a holy site for Catholics like Lourdes in France and resurrect Longbridge.”
Mr Tolkien is probably most famous for his Sentinel sculpture, which stands at the entrance to Castle Vale estate, and features three Spitfires peeling off into the sky in different directions.
He has also sculpted a memorial to the actor Sir Cedric Hardwicke, which has been set up at his birthplace of Lye, West Midlands, for Dudley Metropolitan Borough Council.