The News of the World says Edu has been in talks with Pompey over a move to Fratton Park, where he will join former Gunners team-mates Tony Adams, Sol Campbell, Lauren and Kanu.
Cash-strapped Valencia are desperate to reduce their wage bill and are prepared to offload the Brazilian on a free transfer, even though he has two years of his current contract left to run.
The player himself is keen to return to the Premier League and Edu said: "The interest of English clubs like Portsmouth and Man City is obviously flattering.
"I have amazing memories of the years I spent in England, being the first Brazilian player to win both the Premiership and the FA Cup.
"I feel good at Valencia even after a difficult season but the Premier League is arguably the biggest competition in the world."