The right-back is out of contract at the end of this month and has been in talks with the club over a new deal.
His team ethic, experience and right-back skills would be valuable in a busy season which will include Conference League action ad see key players returning from a summer tournament.
However, leading Dutch football publication and website Voetbal International reckon it looks like he will be on the move.
That would effectively mean a return to what many Albion fans would have been resigned to anyway when he reached the end of the season without a new agreement in place.
Hopes that he would stay on were raised when he was included on the retained list earlier this month after Adam Webster, Solly March and James Milner were let go.
It is said Veltman has no problem with Albion and feels valued by them.
As well his efforts on the pitch, he is also an enthusiastic participant in BHAFC Foundation activities.
But Voetbal International report: “It does appear, however, that Veltman will not return to Brighton after his holiday, although the club is still keeping the door open for him.”
The former Ajax man is said to have offers in Holland and other European leagues.