According to Defensa Central, the Gunners are looking to move Lacazette on before his contract expires next summer and hope to convince Bale to head in the opposite direction.
The French striker arrived at the Emirates from Lyon for £46.5million in July 2017, agreeing a five-year deal which is now coming to an end.
He was soon replaced as Arsenal’s record signing and chief goal threat by Pierre-Emerick Aubameyang, who joined from Borussia Dortmund.
Despite typically playing second fiddle to Aubameyang, Lacazette has still registered 67 goals in 174 appearances across all competitions.
Real Madrid are also known to be in the market for a striker to take some of the goalscoring burden off Karim Benzema.
Their other centre-forwards – Luka Jovic and Mariano – have struggled to cope with expectations at the Bernabeu.
In contrast, Lacazette knows what it takes to perform for a big club at the highest level and would welcome a change of scenery.
If Los Blancos firm up their rumoured interest in the January transfer window, Arsenal could try to make Bale part of the deal.
The Welsh international has strong links to North London rivals Tottenham Hotspur, spending six years there before moving to the Spanish capital.
His importance faded due to injuries and disagreements with the Real Madrid hierarchy, resulting in a return to Spurs on loan last season.
Often a peripheral figure under Jose Mourinho, Bale still managed 16 goals in 34 appearances for his former club.
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