The Manchester Evening News says the Reds are understood to have been tracking the 20-year-old Albanian-born player but have intensified their interest.
United have increased their watch on Ninis in 2010 with a scout checking out three of his matches for Panathinaikos since the New Year.
The Greek spy has been sending favourable accounts to Old Trafford. Ninis is said to be the new rising star of Greece football and has attracted interest from Real Madrid and AC Milan as well as United.
Panathinaikos have a get-out clause in his contract of around £10m but could be persuaded to let their star go for less.
With the possibility of alerting more buyers if Ninis stars in the World Cup, the Reds may step in early as they did with 21-year-old Mexican striker Juan Hernandez.