TMW says City boss Manuel Pellegrini wanted to sign Romero as third-choice keeper behind Joe Hart and Willy Caballero.
But Romero refused such a proposal, despite not being guaranteed a place at Samp.
Manchester United also came in for the Argentine in the afternoon, but refused to meet the keeper's personal terms.
United boss Louis van Gaal wanted Romero as a replacement for wantaway reserve keeper Anders Lindegaard.
For the big stories and the banter follow us on Twitter: @tribalfootball