The Spain U21 international was scouted personally by Guardiola during the season, along with new City goalkeeper and former Benfica teammate Ederson.
Correio da Manha says Grimaldo is a priority target for the City manager now that Gael Clichy is being allowed to leave as a free agent.
Benfica want €35 million for the left-back, which would represent stunning business for the Portuguese giants.
Grimaldo was snapped up two years ago from Barca for just €1 million.
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