The Reds will now stay put on Trentside following England's defeated bid to host the 2018 World Cup.
Arthur told BBC Radio Nottingham: "There are no plans to redevelop the Main Stand in the near future.
"Our priority as a club is to try and get back to the Premier League and then to stay there."
Had England's bid been successful, Nottingham would have been one of 12 cities hosting the World Cup, with Forest moving to a new 45,000 capacity stadium.
The Main Stand first opened in 1965 and is the oldest of the four stands at The City Ground. It had to be partially rebuilt three years later following a fire during a [then] Division One game against Leeds United.
"We are incredibly reliant on the financing from [owner] Nigel Doughty and it is not something as an executive that I am particularly comfortable with.
"We're very grateful, but we would like to have a sustainable business model in the Premier League and that is our aim and ambition."
Source: BBC Sport
Source: BBC Sport