The Spurs chief is believed to be looking to draft in at least two centre-forwards over the summer, after a lack of firepower contributed to his side missing out on Champions League qualification.
Scouts from the London club have been watching the Spaniard recently, and the reports they have returned to AVB appear to have convinced him to press ahead with a move.
Benfica are said to value the attacker at around £10m, a figure the White Hart Lane side could easily match.
The 22-year-old, who was born in Brazil, spent a brief stint in the Premier League during the 2010/11 season, signing on loan with Bolton from the Lisbon side.
Rodrigo’s ability to play across the frontline is another factor that appeals to AVB, who is keen to add strength and depth to his squad.
Meanwhile, Spurs are also keen on Barcelona striker David Villa, who has been attracting the attention of north London rivals Arsenal.
Internacional star Leandro Damiao is also on the club’s radar, and they could return with a fresh bid after seeing an offer for the Brazilian rebuffed in January.
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