Real Madrid have agreed personal terms with Arsenal captain Patrick Vieira over a potential move to the Spanish club, newspaper Marca have reported on their website.
Real, who confirmed their interest in Vieira on Tuesday, are now ready to talk to Arsenal about a fee for the 28-year-old French midfielder, Marca said.
Real Madrid have signed one world-class player each season since Florentino Perez took over as club president in 2000, starting with Luis Figo and continuing with Zinedine Zidane, Ronaldo and David Beckham.
On all four occasions, Real have done deals with the players first before going on to talk to the clubs.
Perez was re-elected Real president earlier this month and has promised to continue his policy of bringing in one 'galactico' per season.
Emilio Butragueno, Real Madrid's director of football, confirmed on Tuesday the club were interested in signing Vieira.
"Yes, he's a very interesting player and he's very important for us and our club," Butragueno said when asked whether his club were trying to sign the France international.
"We're not there yet. It's a long process... I think this week will be decisive," the former Spanish striker told Reuters in Tokyo, where Real Madrid are due to play against two J-League teams as part of a pre-season tour.
Real imploded at the end of last season, losing the King's Cup final, going out in the quarter-finals of the Champions League and losing their last five league games on their way to a fourth place finish.
Perez has already spent 25 million euros (17 million pounds) to sign Argentine centre-back Walter Samuel from Roma in an attempt to solve the team's evident problems in defence. Vieira is now wanted to give the midfield a more solid look.