The Daily Star says United are thought to have offered an initial £12.5m bid for the centre-back, who they view as an ideal replacement for Rio Ferdinand.
But Benfica have told United they want £25m before they'll consider selling the 26-year-old.
The Lisbon-based side owe Garay's former club Real Madrid a percentage of any transfer fee, so will hope to extract as much cash out of United as possible.
Old Trafford scouts flew out to Portugal last week to watch Garay in his side's clash with rivals Porto.
Although United are unlikely to tie up a deal for the Argentina international this month, Sir Alex Ferguson is keen for Garay to join in the summer.
According to Marca, Garay would jump at the chance to join United and agreement on a fee between the two clubs is the only stumbling block to any deal.