Vinicius, 25, is expected to join on a season-long deal with an option to make the move permanent for around £40million next summer, provided he is granted a work permit.
Mourinho has been desperate for an alternative to Harry Kane since his appointment in November and complained he "had nobody" up front for Tuesday's Carabao Cup win over Chelsea.
Ahead of Thursday's Europa League play-off against Maccabi Haifa, the Spurs manager said he was "optimistic" of signing a forward and claimed the club was "trying everything".
Vinicius, 25, joined Benfica from Napoli for £15m in summer 2019 and scored 25 goals last season.
Benfica resolutely rebuffed interest in their best players at the start of the summer but the Portuguese club's failure to qualify for the Champions League has forced a rethink and they have also sold centre-half Ruben Dias, another player admired by Mourinho, to Manchester City this week.
The arrival of the uncapped Brazilian would not impact Gedson Fernandes, who is also on loan from Benfica until the end of the season and started Tuesday's derby, because Premier League clubs are permitted to loan two players from the same foreign team.
At 6'3", Vincinius, who is represented by Mourinho's longtime associate Jorge Mendes, offers the physical presence desired by the Spurs boss in a centre-forward but he is versatile enough to play on the wing, having also bagged 13 assists last season.
His arrival would take Tottenham's summer spending well beyond £50m after the captures of Matt Doherty for £15m, Sergio Reguilon for £27.5m and Gareth Bale, whose season-long loan will cost roughly £10m in wages.
Mourinho still wants a centre-half before the close of the transfer window and Chelsea are prepared to let Antonio Rudiger join Tottenham on loan. Spurs are also considering a late bid for Inter Milan's Milan Škriniar, and have watched South Korean international Kim-min Jae.
The club must also offload unwanted players. Juan Foyth is interesting Villareal, while Danny Rose and Paulo Gazzaniga can also leave permanently.
England youth internationals Ryan Sessegnon and Jack Clarke are expected to be sent on loan.
Mourinho has ruled out allowing Dele Alli (below) to leave and has opened the door for him to return to the squad for Thursday's one-off home play-off against the Israeli side, saying he has been impressed with the midfielder's professionalism in training.
Alli was left out of the 18 for the fourth time in five matches against Chelsea and Mourinho has challenged the 24-year-old to prove he deserves a place in the side.
"He's being very, very professional – I have only respect for him," Mourinho said. "Particularly on Tuesday when the team was preparing for the game and he wasn't. It would be perfectly acceptable to have a lack of motivation, even a lack of professionalism for this training session but it was exactly the opposite. He trained very hard. He has my respect and the respect of his teammates so it's possible he plays."
The Portuguese will be without injured forwards Heung-min Son and Gareth Bale, with the pair expected to return after the international break, while he has said Eric Dier and Erik Lamela will not be involved after playing 90 minutes on Tuesday. Kane is expected to start.
Maccabi's chief executive on Wednesday night apologised to Tottenham for a viral video of the one of their players, Abu Fani, taunting Kane.
"Our club condemns such behaviour," said Assaf Ben-Dov. "We are a club that advocates the person before the player. I would like to take this opportunity to apologise to Tottenham and Harry Kane, who we greatly respect.