The Premier League rivals sent scouts to watch Porto in action during their 3-2 win over Portimonense on Friday night, when the hosts needed two goals in injury time to emerge victorious.
A 91st-minute strike from Vincent Aboubakar was followed by a dramatic Yacine Brahimi winner five minutes later to send Porto through to the next round of the cup, with Danilo having got his own name on the scoresheet earlier in the game.
Arsenal have been linked with the 26-year-old in the past, while Jose Mourinho regularly keeps tabs on players from his former team.
The player, who was part of Portugal's Euro 2016-winning side, has also been linked with Paris Saint-Germain in the past, so the Premier League duo could face competition for his signature.
Danilo has scored twice and assisted one more in his 14 appearances for Porto across all competitions this season.