Louis van Gaal says Manchester United have offered David de Gea "a lot of money" in a bid to keep him at Old Trafford.
Bruce was dealt a blow late on Monday evening when the 24-year-old Burnley forward failed a medical, leaving him to start the search for attacking reinforcements all over again.
However, having completed deals for Allan McGregor, Maynor Figueroa and Curtis Davies, and secured the permanent transfers of loan signings Ahmed Elmohamady and George Boyd, the Tigers manager is satisfied with his lot to date.
He told the club's official website, www.hullcityafc.net: "So far, we have brought in three quality players to add to the existing squad.
"We will be doing our best to add more to that, and we aren't finished yet by any stretch of the imagination. We will keep working away at it.
"We have also turned a couple of last season's loans into permanent deals in Ahmed and George and that was important.
"Elmohamady was our Player of the Year last season, so the first piece of important business was to get his transfer over the line and we did that, in the same way that we secured [Robbie] Brady and [David] Meyler midway through last season.
"We are very pleased with what we have got so far. We will add one or two more to make us bigger, stronger and better, and to make us better equipped for the challenge ahead."
Burnley striker Austin was poised to become the latest addition until medical tests revealed a problem, prompting Hull to reluctantly pull the plug on the deal.
Bruce said: "We are disappointed with what happened with Charlie on Monday, of course we are.
"It's disappointing for us, but we are more disappointed for Charlie, believe me.
"It was an awful situation for him to find himself in and we do wish him all the best."
Bruce is now back in harness after enjoying his summer break - or at least that part of it which he did not spend on the telephone - and is relishing the opportunity to ply his trade in the Barclays Premier League once again.
He said: "I have had a great summer, although a manager's work is never done because the phone never stops ringing.
"But it's been a good break and now we have got a big challenge ahead. We are where we want to be and we are all in the game to be at the top level.
"The season is getting closer and it's less than six weeks away. I'm sure everybody is just as excited about it as we are and as I am, and is relishing what will be the biggest challenge we have had for a long time."