The Premier League champions are believed to be interested in the 20-year-old, as manager Roberto Mancini prepares to overhaul his squad over the summer months.
A powerful central man is said to be on his list of priorities, a set of requirements matched by Kondgobia.
The Frenchman has been attracting much interest from across Europe thanks to a series of impressive performances in La Liga for the Andalusians
City are one of the parties monitoring the situation, and are rumoured to be willing spend big to secure a deal.
Kondogbia only signed for Sevilla last year and has a contract at the Ramon Sanchez Pizjuan Stadium which runs until 2016.
As a result, the Spaniards are demanding a high fee with the knowledge that they do not have to rush to sell.
Mancini is thought to be unconvinced by a number of his midfield options, including pre-season signings Jack Rodwell and Javi Garcia.
As a result he could look to move the players on sooner rather than later.
The Italian has also been linked with a move for Celtic’s Victor Wanyama, who has been impressive for the Bhoys this season.