Julien Fournier, the French club's general manager, insisted at the weekend that the left-back would not be heading to San Siro.
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 UEFA Champions League qualification.
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.