The Premier League side have been chasing the Frenchman for some time and are expected to make a summer move, as manager Arsene Wenger steps up his plans to improve his defensive line.
But, they will face a tough battle for Rami, who is attracting serious interest from the mega-rich Dagestan-based outfit Anzhi.
The Russians lost Christopher Samba to QPR at the end of January, and are yet to have found an adequate replacement.
This has led to rumours that they are willing to offer the 27-year-old an extremely lucrative deal, £3m-per-year, to leave the Mestalla.
Also, they are reportedly ready to hand around £13m to Valencia, a figure they will find hard to refuse due to their well known financial difficulties.
This news will come as a blow to the Gunners, who will be unlikely to match Anzhi’s offer in terms of financial reward.
Wenger is believed to have highlighted his defence as a particular area of concern, after watching Thomas Vermaelen and Per Mertesacker struggle for the majority of the season.
There are rumours that the Frenchman has been tracking Rami since his spell in Lille, and is willing to allocate a large chunk of his transfer budget this summer to push through a deal.
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