Nice had been adamant that the left-back would not be allowed to leave the club although the Serie A side are now closing on completing a deal
Dalbert has arrived in Milan for a medical ahead of an expected switch to Inter from Nice.
Julien Fournier, the French club's general manager, insisted at the weekend that the left-back would not be heading to San Siro.
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However, Inter tweeted images of the Brazilian undergoing a medical on Tuesday, suggesting a move is not far away.
Dalbert signed for Nice from Vitoria de Guimaraes last year and made 33 appearances as they finished third in Ligue 1, securing Champions League qualification.
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Lucien Favre's men will take on Napoli in the play-off round of that competition after seeing off Ajax in the third-qualifying round.
Inter have been busy in the transfer market, with Matias Vecino, Milan Skriniar and Borja Valero among their acquisitions ahead of the new season.