The Daily Mail says the White Hart Lane chairman flew to Spain on Monday with agent Dennis Roach and finance director Matthew Collecott to meet Real president Florentino Perez.
No agreement has yet been reached but talks continue.
Real have circulated a list of nine players who are available for transfer, but Spurs are concerned by the high salaries demanded by their targets.
While former Chelsea winger Robben, 25, is reluctantly accepting his career at Real is over after the acquisition of Cristiano Ronaldo and Kaka this summer, he only wants to go to a Champions League club.
Striker Huntelaar, also 25, has the predatory instincts Redknapp demands, but the Tottenham boss must sell first.