The 27-year-old defender has been heavily linked with a move to the Premier League in recent months, after he spoke of his desire to play for a "big European club".
Gunners boss Arsene Wenger is credited with an interest in bringing the France international to the Emirates Stadium, amid speculation linking current centre-back Laurent Koscielny with a move away from north London this summer.
Meanwhile, Manchester United are also monitoring Rami's situation, and are believed to be ready to meet the player's £12.5million valuation in order to sanction a transfer to Old Trafford.
Rami has built a reputation as one of the most highly rated defenders in La Liga, after arriving at the Mestalla from Lille back in 2011.
However, with Valencia crippled by growing financial debts, they might be forced to sell one of their star players, particularly as the club looks set to miss out on European qualification.
Manchester United have ensured their place in next season's Champions League, having already claimed this year's Premier League title, while Arsenal's hopes of a top four finish still hang in the balance.
Rami remains happy in Spain but will be tempted by the opportunity to test himself in Europe's elite club competition, should the prospect of a transfer arise at the end of the summer.