The Brazil international joined United in a £17.5million deal from Porto in 2007.
The 22-year-old has been struggling with injuries and a loss of form over recent seasons.
“I am good in Manchester but I’d like to return to Portugal and my preference would be Porto. I love the country,” said Anderson.
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Since Guus Hiddink arrived at the helm, Chelsea have improved considerably after a tricky start to the campaign.
Newcastle United are staring down the barrel of relegation to the Championship for the second time in the past eight years.