An agreement in principle is in place between new Premier League champions United and the Lisbon giants for the 26-year-old, according to reports in Portugal.
United signed Uruguayan full-back Guillermo Varela, 20, this week, and could follow that up with the ?17million capture of Argentina international Garay.
Although Rio Ferdinand has signed a one-year contract extension, he will turn 35 later this year.
There are ongoing doubts over the future of United skipper Nemanja Vidic and Chris Smalling and Phil Jones were plagued by injuries last season, so incoming United boss David Moyes wants defensive reinforcements.
Source: DSG
Source: DSG