Van Dijk was the matchwinner for Liverpool on his debut in the FA Cup third round Merseyside derby win over Everton but the trip to the Liberty Stadium could represent his first top flight outing since his world-record £75m (€85.1m) move from Southampton.
Captain Jordan Henderson and full-back Alberto Moreno were also present at the session after respective spells out through injury.
England international Henderson has missed the last five games with a hamstring injury picked up in the 3-3 draw with Arsenal before Christmas, while an ankle problem has kept Moreno sidelined for six weeks.
It remains to be seen whether the trio will be fit to face bottom club Swansea, managed by Carlos Carvalhal, but it could hand coach Jurgen Klopp a selection dilemma for the game.
Van Dijk will compete with Joel Matip and Dejan Lovren for a starting berth in defence, while Klopp will have to decide whether Georginio Wijnaldum, Emre Can or the in-form Alex Oxlade-Chamberlain makes way for skipper Henderson.
Meanwhile, the German coach will have to weigh up whether Andrew Robertson's recent performances have been good enough for him to keep out Moreno, with the Spaniard having been first choice until his injury.
One decision Klopp has already made is in Liverpool's problem position in goal, where Loris Karius will remain after being recalled for the win over Premier League leaders City.
The 24-year-old had played just three times in the top flight this season before being selected over Simon Mignolet – whose future on Merseyside is riddled with uncertainty – for the game, with Klopp having pledged to give his fellow countryman a run in the team for an extended period.
Karius began his spell as the Liverpool number one in ignominious fashion as he allowed Leroy Sane's rasping drive to beat him at the near post during the seven-goal thriller against City, but it remains to be seen how he copes with being the main custodian at Anfield.