Romero, 50, goes into the final round attempting to surpass Irishman Des Smyth as the oldest winner in European Tour history. Smyth won the 2001 Madeira Island Open at 48 years, 34 days.
Romero, defending champion Remesy (67) and Van de Veld (70) are at 9 under for the tournament.
'The important thing is I'm in that final group. That is what I wanted. I feel fit and strong and ready for one more day,' said Romero.
Remesy had an eagle and four birdies in his round, but carded his lone bogey on the final hole.
Denmark's Soren Hansen and England's Jonathan Lomas both shot 71 and are one stroke off the lead.
Jose Maria Olazabal is five strokes back after a 70, and Colin Montgomerie, who also shot 70, is seven back.
More than just a title is riding on the result Sunday. With a top-two finish, Romero would gain an automatic exemption from having to qualify for the British Open. Van de Velde needs a top-four finish to be assured of securing his European Tour card for 2006.