CPPI said it had not yet appointed a contractor for the job at Bridgewater Place in Leeds.
Plans to install screens outside the 32-storey building were backed by councillors in November.
Dr Edward Slaney was killed next to the building in March 2011 when a lorry was blown on top of him by the wind.
Wind speeds of 67-79mph were recorded at the building that day.
The construction scheme includes erecting three sail-like structures across Water Lane as well as screens and canopies.
The large screens and baffle boards to deflect the wind - up to 50ft (17m) high and 66ft (20m) long - are to be built near the building and above the road.
The coroner at Mr Slaney's inquest recommended Leeds City Council close the roads around the building when wind speeds reach about 45mph.
The building's owners, CPPI Bridgewater Place Limited Partnership, said: "We are currently undergoing a complex and lengthy tendering process to find a suitable contractor."
The owners said it would provide more information and a detailed construction timetable in the "coming months".
The owner of Yorkshire's tallest building has announced construction work to deflect strong winds is scheduled to start in August.