The 21-year-old midfielder has departed the Portuguese club's base in Como, Italy, and travelled to the Algarve, where Forest are holding their own pre-season camp, with the Portugal Under-21 international expected to undergo a medical before signing a long-term contract in a deal worth €20m (£17.3m).
Sá is represented by Jorge Mendes, whose relationships in Portuguese football, along with those of Olympiacos football director António Miguel Cardoso, are understood to have helped smooth the move. Once completed, the transfer will rank as the biggest sale in Famalicão's history, eclipsing the fee received for Manuel Ugarte's move to Sporting.
Sá captained Famalicão to a fifth-place finish in the Primeira Liga last season, the club's highest league position of the century, contributing four goals and two assists in 34 appearances despite his relative youth.
That level of performance is what convinced Forest to move for him, though he is not expected to go straight into Nottingham's first-team plans: once his transfer is finalised, he is instead set to spend at least the first half of the season on loan at Olympiacos, gaining regular football before stepping up to the Premier League.
The Greek club and Nottingham Forest are both owned by Evangelos Marinakis, whose wider ownership group also includes Rio Ave, and the loan fits the pattern of development moves the group has used previously to ease young signings into English football.
The move brings an end to a saga that appeared to be heading in a different direction only weeks ago, when West Ham looked to have won the race for Sá's signature at the same €20m fee before their interest stalled following relegation from the Premier League.
For Famalicão, the fee represents a significant windfall for a player who joined their academy as a teenager; for Forest, it secures one of Portugal's most highly-rated young midfielders while immediately giving him a route to continued development away from Trentside.