Portugal U21 worldwide Dalot is understood to have a €20m (£17.4m) release clause in his Porto contract - which expires next summer - and is thought to have attracted interest from some of Europe's leading clubs.
Dalot, who has already agreed personal terms, has made only a handful of first-team appearances for Porto after breaking into their team last season when he featured against Liverpool in the Champions League.
Strengthening his defence is a priority and a new right-back to act as a long-term replacement for Antonio Valencia is desperately needed as the Ecuadorian worldwide turns 33 in August.
Dalot has represented Portugal from under-15 to under-21 level and made his Porto debut in October.
Meanwhile, the former Porto player's arrival implies that Mourinho will be letting the likes of Daley Blind and Matteo Darmian leave in the summer.
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Manchester United are reportedly interested in Barcelona left-back Jordi Alba.
Ashley Young, primarily a winger, was used at left-back on numerous occasions last season, but the United boss is said to want a more traditional defender on the left side of his back four.
Manager Mourinho is keen to make moves quickly in this summer's transfer market, with the earlier closure on August 9 giving the club three fewer weeks to do deals compared to previous years.
Matteo Darmian is set to join Juventus, while Dutch global Daley Blind is unlikely to still be a United player by the start of the new season.
The player's agent has criticized the club after they failed to live up to their promise of handing the defender a new contract. "But we are still waiting".