Celtic are on the look out for a new striker, following the appointment of Brendan Rodgers as manager.
Celtic have already brought in Moussa Dembele from Fulham, but Rodgers feels that more additions are needed to give him sufficient firepower at Parkhead.
Veldwijk could be available this summer, as he has struggled to make an impression at Forest.
The 24-year-old moved to the Reds back in 2014, but he has failed to force his way into the team at the City Ground.
Veldwijk has only made 11 Championship appearances for Forest, and he has failed to score in any of them.
The Dutchman was sent out on loan to PEC Zwolle last term, and he was more successful.
Veldwijk netted 14 times in 33 appearances while back playing in his homeland, and Rodgers has reportedly seen enough in the target-man to suggest he could be a good addition for Celtic.