According to the Mirror, scouts from the Catalan club monitored the 26-year-old during Holland clash against Sweden last week and Barcelona are now weighing up the opportunity of tabling an offer for the centre-back during the January transfer window.
The Dutch international was keen on completing a switch to Anfield in the summer transfer window. Earlier in June, the deal was all but set to take shape, before the Saints reported the Merseyside club to the Premier League for an alleged illegal approach.
Liverpool were forced to issue a public apology for any "misunderstanding", even though Van Dijk remained interested in joining Klopp's side and even handed in a transfer request.
His request was instantly rejected by Southampton, who forced Van Dijk to train away from Mauricio Pellegrino's first-team for the remainder of the transfer window, before making his first start before the international break, as Southampton lost 2-1 to Stoke City.
The south coast club do not want to sell Van Dijk but it is understood that, should they opt to allow him to leave, they would rather sell him abroad than to another Premier League club.
Liverpool's failure to sign the Dutchman has made its impact felt, as the Reds' back four has come under intense criticism for a series of mistakes that have cost the team points. Jurgen Klopp's men have already conceded 12 goals in their first eight league games and only Watford, West Ham, Stoke and bottom-of-the-table Crystal Palace have conceded more.
Should Barcelona follow up their interest in Van Dijk, Liverpool could face a fight to secure one of their main targets.
The two clubs spent locked horns throughout the summer, with the Reds resolutely refusing to allow Philippe Coutinho to move to Barcelona.
Despite making multiple bids and the player himself putting in a transfer request, the Catalans failed to land the Brazilian playmaker as Liverpool stood firm on their stance that Coutinho was not for sale.
However, earlier this week, the four-time European Cup winners hinted they would bid for 25-year-old again, with the club's CEO Oscar Grau claiming Barcelona were "financially ready" to sign Coutinho but the technical staff will have the final say over whether it is necessary to bring in the Liverpool star or any other player during the coming January transfer window.