The Dutch newspaper claim on their website that the Hammers have made contact with the 27-year-old’s representatives ahead of a possible summer transfer.
De Telegraaf report that it is doubtful that Veltman will remain at the Johan Cruijff ArenA next season, with the defender admitting he is ready to leave the club.
Veltman failed to make much of an impact at Ajax last season because of injury, and only made nine appearances in the Eredivisie, four of which were starts.
He did make five Champions League appearances though and played both legs against Liverpool in the semi-finals.
It is hard to see where Veltman would fit in at West Ham, who already have a settled starting defensive set-up. Both Fredericks and Zabaleta featured throughout the previous Premier League campaign, and the experienced Argentinian recently signed a new one-year deal at the Hammers, cementing his place for at least an extra season. With two solid options already available to Manuel Pellegrini at right-back, the Chilean must have a different plan in place for Veltman, with cover in central defence possibly high on his agenda this summer. The 27-year-old struggled for game time last season and could settle for a lesser role as he tries to prove his fitness in pre-season. Bologna were reported by Calciomercato to have ended their pursuit of Angelo Ogbonna, meaning the signing of Veltman could leave Pellegrini with too many options in defence. With Winston Reid also returning from injury, it appears that the Hammers have all the cover they need, and a move for Veltman could even see one of their defenders exiting the club in the next month or so.