Nelson, who spent last season on loan at Fulham, has been the subject of interest from a number of clubs across Europe.
The 25-year-old has now decided to join Brentford and is set to undergo a medical before the transfer window shuts tonight.
Standard Sport understands that Brentford have the option to make the move permanent at the end of the season.
Nelson made a strong start to his loan at Fulham last season, featuring in 12 of their first 14 Premier League games, before a hamstring injury ended his campaign in December.
Fulham had been considering making a move to bring Nelson back to the club, with Silva a long-term admirer of the Englishman.
Crystal Palace had also been tracking Nelson and Standard Sport had reported how the winger’s preference was to stay in London.
They have already brought in club-record signing Dango Ouattara to replace Bryan Mbeumo and Nelson is expected to provide cover for Kevin Schade on the left wing.
Brentford are still expected to sign a striker before tonight’s deadline and saw a £45million bid for Borussia Dortmund’s Maximilian Beier rejected last week.
It’s been a summer of upheaval for Brentford who are set to lose Wissa as well as Mbeumo and captain Christian Norgaard, who departed the club earlier in the window.
