The 27-year-old centre-back has been heavily linked with a move away from the Mestalla this summer, despite the fact he is under contract in Spain until 2015.
Red Devils boss Sir Alex Ferguson has been credited with an interest in bringing the France international to Old Trafford, and is ready to steal a march on long-term admirer Arsene Wenger, who is also keen to add Rami to his Gunners ranks.
With a €25million buy-out clause written into his current deal at Valencia, both Manchester United and Arsenal know exactly what it will take to activate negotiations about a possible transfer.
Rami is regarded as one of the most consistent defenders in La Liga at the moment, and has made 35 appearances for Valencia in all competitions in 2012/13.
The former Lille star has already gone on record telling Le Parisien that he needs to play for a big European club, so a move to either Manchester United or Arsenal will tempt the centre-back when the transfer window reopens on July 1.
Ferguson has also been linked with a number of other central defenders, with Real Madrid's Rafael Varane and Benfica's Ezequiel Garay both reportedly under consideration by the Premier League leaders.