Bruce, who was appointed the Newcastle manager in the summer, was in charge of Hull from 2012 until 2016, while Netherlands international central defender Van Dijk was on the books of Celtic from 2013 until 2015.
Newcastle will take on Liverpool away from home at Anfield in the Premier League on Saturday afternoon.
Bruce told The Guardian: “I could have taken him [Van Dijk] to Hull. I had dinner with Kenny Dalglish and the owner of Celtic, Dermot Desmond, in Barbados – I’m name-dropping now –and Desmond was waxing lyrical about the best players he’s had.
“He was saying: ‘[Henrik] Larsson is definitely, definitely the best I’ve seen play for Celtic in my ownership but what I can’t understand is nobody has gone for Van Dijk.’
“I thought: ‘That’s interesting, he’s seen a lot of football over the last 12 years,’ so I tried to get him before he went to Southampton but I had no chance.”
Van Dijk is one of the best defenders on the planet and is a world-class footballer, and there is no doubt that the Dutchman would have been a brilliant signing for Hull.
The 28-year-old left Celtic for Southampton in the Premier League in 2015 and is now at Liverpool, where he won the Champions League last season and also finished second in the Premier League table.
According to the CIES Football Observatory, Van Dijk is now valued at €120 million (£107.05m).
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