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.