However, the Seagulls were unable to match the €3 million (£2.6m/$3.4m) transfer fee that would have been required to seal the Netherlands international's services.
Having transferred to Anfield from St Mary’s Stadium for a reported fee of £75m ($98m) – a world-record for a defender – in January 2018, the 27-year-old has established himself as one of the best centre-backs across the globe.
He was awarded the PFA Player of the Year Award last month for his efforts under Jurgen Klopp that have driven Liverpool to a title charge and a second successive Champions League semi-final.
Now, however, Poyet, who managed Brighton between 2009 and 2013 in his first main managerial role, has revealed that Albion considered picking up the defender early in his career.
At the time, the club had just sealed promotion from League One in a title-winning 2010-11 campaign and were preparing for life in the Championship.
Speaking to talkSPORT, Poyet admitted that he went to observe Van Dijk as a potential new recruit – but budgetary concerns put paid to any potential move.
“I went to see Van Dijk at Groningen when I was coach at Brighton,” Poyet told Alan Brazil’s Sports Breakfast.
“We went all the way up to Groningen to watch the game, and it was too easy for him. He was already incredible.
“After ten minutes you could see that he was bigger than everyone, more powerful than everyone and so calm on the ball.
“We watched the whole game and afterwards we talked to the chairman and we started getting in contact with the club and the agents, but he was too expensive for Brighton. He was €3million at that time!”
“Brighton had just come into the Championship, although a year later we spent €3m on a striker, Leonardo Ulloa, but for a defender at that time it was impossible.”
Van Dijk and Liverpool face a double challenge over the next few weeks as they look to overcome Barcelona to reach a second Champions League final in as many years, as well as clinch a maiden Premier League crown over rivals Manchester City.