Vitor, 20, is represented by Israel super-agent Pini Zahavi, who persuaded Pompey owner Ali Al-Faraj to reappoint former Chelsea boss Grant.
Zahavi has recommended the right back to the Portsmouth director of football.
Grant, who returned to Fratton Park as director of football last month, is ready to take Vitor on loan in January once Pompey's transfer embargo is lifted.
The defender's Benfica's team-mate Hassan Yebda is already on loan with the Premier League strugglers, who eased their immediate concerns with a 4-0 whipping of Wigan on Saturday.
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