"We had huge, huge difficulties with email and faxes so we hope a little commonsense prevails," said Bruce.
The Black Cats boss is eager to add more firepower to his struggling side, who have not won in 11 league games.
Benjani, 31, is a free agent in the summer but City boss Roberto Mancini has said he can move on now if he wants to.
"I think we've lodged everything in time, we've done everything we possibly can and I'm convinced we had everything in in time," Bruce told reporters after Monday night's 0-0 draw with Stoke.
"The paperwork was lodged but we had some huge, huge difficulties and we informed both the Premier League and the FA at the time of those.
Is Benjani the right man for Sunderland?
"We wait to find out but I hope we are granted the player, who would be a huge boost to us."
Benjani joined City from Portsmouth in January 2008 but has spent long spells on the sidelines with injury and struggled to establish himself in the first team, starting just 21 games in two years.
Source: BBC Sport
Source: BBC Sport