The Premier League champions are understood to have first refusal on the Uruguayan until June 6 to meet the Italian club’s £14.4 million (€18m) asking price.
City manager Roberto Mancini is an open admirer of Ramirez and could be ready to step up his interest in the playmaker after missing out on Lille star Eden Hazard, who has announced his intention to join Chelsea.
"Ramirez? He is a good, young player with great potential," Mancini told Gazzetta dello Sport this week. "In attack, though, we are OK."
City could also be in the market for another attacking player with growing talk in Germany that Edin Dzeko is being lined up by Bayern Munich for a summer move.
Ramirez, 21, is considered one of the most exciting attacking players in Italy and his agent, Pablo Betancourt, has been authorised to hold talks with Tottenham over a switch to White Hart Lane.
Spanish club Malaga have also been linked with a move for Ramirez while Liverpool made contact with Bologna before the Anfield club’s American owners sacked manager Kenny Dalglish.
Ramirez is under contract with Bologna until 2016 but is almost certain to leave this summer should he get the chance to join a Champions League calibre club.
"It's very probable that this will have been his last season at Bologna," Betancourt said earlier this month.
"We already have a few offers, but we will speak with Bologna officials at some point after June 1."
Ramirez scored eight goals and provided six assists in Serie A last season and has been capped nine times for Uruguay.