A planning application, submitted by the Inner City Trust, aims to see the building repurposed into a community hub.
Brian Tierney says after 14 years as a councillor the time is right for him to step aside in 2027.
The former Convent of Mercy on Pump Street in Derry was damaged in Storm Amy in October 2025
McHugh has been a representative for the West Tyrone constituency at the Northern Ireland Assembly since 2019.
Derry City and Strabane District Council is stepping up preparations for the final bid to be submitted by the end of November.
Work to restore the memorials in Londonderry, Castlederg, Sion Mills and Strabane will begin on Monday.
The report explores the movement of some families from the Cityside to the Waterside between 1968 and 1998.
A record 1,013 teams from across the island of Ireland, the UK, Europe and North America are taking part in this year's competition.
