Manchester City reportedly rejected moves for Virgil van Dijk and Harry Maguire as they were not prepared to pay world-record fees for the pair in either January 2018 or the recent transfer window.
Liverpool spent £75m on Van Dijk at the mid-point of the 2017-18 campaign, while Manchester United broke the world transfer record for a centre-back when they signed Maguire from Leicester City in the summer.
City have problems in central defence this season, with Aymeric Laporte on the sidelines following knee surgery and Vincent Kompany moving on during the summer to take up a player-coaching role with Anderlecht.
John Stones and Nicolas Otamendi struggled during the team's 3-2 loss at Norwich City on Saturday, and the former is now facing six weeks on the sidelines with a thigh problem.
According to The Guardian, head coach Pep Guardiola had wanted to sign Van Dijk and Maguire when each player became available, but the Premier League champions refused to meet Southampton's or Leicester's asking price.
Kyle Walker and Fernandinho are both options for Guardiola to plug the gap until Stones returns to fitness - at which point the champions could have lost further ground in the Premier League table.
