The France star is thought to be keen to leave Spain, and his La Liga employers are willing to part with the defender in exchange for a fee in the region of £7.75m.
Arsenal and Manchester City were initially quoted as much as £21.5m for the centre-back, but his price has dropped after Rami's £10m buyout clause became public knowledge.
And the report claims the price drop could spark renewed interest from City and Arsenal, with both Premier League clubs eager to strengthen their defences.
Rami would offer proven Champions League experience, and could slot into both teams relatively comfortably after two years with Valencia.
But Arsenal and City's pursuit of the 27-year-old could be complicated by interest from big-spending French club Paris St Germain.
Rami spent five successful seasons in Ligue 1 with Lille before making the switch to Spain, and the French champions are believed to be monitoring developments.
He's still very highly rated in France, and PSG would be more than a match for City and Arsenal financially.
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