The England defender, 25, was close to joining Liverpool on transfer deadline day in September before the move collapsed.
Other clubs reportedly interested in Guehi, including Liverpool once again and Bayern Munich, were understood to be targeting a move at the end of the season, when Guehi was due to be a free agent.
Sky Sports said the move was in the 'final stages' and it would be worth around 20 million pounds.
Pep Guardiola, speaking on the eve of City's match against Manchester United, was tight-lipped when asked about the club's potential interest in Guehi, stressing he had "nothing to say".
Guehi captained Palace to FA Cup success in May against City and has won 26 England caps.
City boss Guardiola, whose team are second in the Premier League, six points behind Arsenal, said the team were desperately short of defensive options.
"Without John (Stones), without Ruben (Dias), without Josko (Gvardiol), we are in a difficult situation for not one game but a long, long period," he said.
"It's a difficult situation. Ruben will be back soon. Josko, no. John, hopefully we'll see."
It's another big blow for Palace, who, on the same day they are likely to lose their captain, manager Oliver Glasner also announced his intention to leave the club at the end of his contract in the summer.