Arsenal have been reportedly alerted by the availability of Karim Benzema, after Real stepped up their interest in Atletico Madrid striker Radamel Falcao.
Falcao is on the radar of some of the biggest clubs in Europe, with Chelsea and Manchester City considered as the frontunners. However, it is understood, Falcao would prefer a move to Real if they showed a firm interest and the Spanish La Liga champions will need to sell one of their star strikers - Benzema or Higuain - to procure funds for a transfer.
Arsenal manager Arsene Wenger is a long-term admirer of the French international, but the chance of a move remains slim, with Arsenal reportedly closing in on another Atletico striker Adrian Lopez.
Benzema, also, played down the suggestions of a transfer. "The coach (Jose Mourinho) has worked hard with me on the mental factor of my game," he said. "Now I'm stronger in this regard. I've had many ups and downs since I came to Madrid, but I'm still here.
"Jose Mourinho is a great coach and very supportive. Pressure has been part of my life since I was in Lyon, but here it is more intense because I'm at the best club in the world."
Lopez remains the most likely signing for Arsenal in January, with Fernando Llorente of Athletic Bilbao also a distinct possibility.
Meanwhile, Arsenal midfielder Jack Wilshere starred for the under-21 side in their 2-1 victory over Everton Monday.
The playmaker, who has not played a competitive senior game for well over a year, was instrumental in bot of Arsenal's goal and played the full 90 minutes as one of England's brightest stars steps up his comeback into the first-team fold.
Arsenal were insipid against Norwich Coty last weekend, and despite having the likes of Santo Cazorla, Mikel Arteta, Aaron Ramsey and Lukas Podolski in their side, they were crying out for a player to show a lot more desire to carve open the defense, something that Wilshere is best at.
The 20-year-old was at the heart of almost every Arsenal attack, excelling in a playmaking role against the Everton udner-21 side.
Wilshere started the move for the first goal, playing in Jernade Meade, who in turn, cut the ball back for Thomas Eisfeld to score.
Wilshere then garnered the assist for the Gunners' second goal - playing the perfect ball for Eisfeld to score his second.
Bacary Sagna and Emmanuel Frimpong also played the full 90 minutes, giving Wenger further encouragement ahead of a crucial run of matches.