The 20-year-old has attracted interest from a wide range of different clubs from across Europe, with the Premier League believed to be his most likely destination this summer.
Kondogbia only signed for Sevilla from French side Lens last year, and has already established a reputation as one of the brightest young prospects in La Liga at the moment.
David Moyes is understood to be keen to bring the France youth international to Old Trafford, as he aims to strengthen his recently inherited squad from Sir Alex Ferguson.
Despite his valuation of £15million, Manchester United believe they can sign Kondogbia for around £8million, and would be willing to loan the player back to Sevilla for the 2013/14 campaign.
The box-to-box midfielder recently said that Stamford Bridge would be his preferred choice of transfer if he were to move to England, but that hasn't deterred the Premier League champions from attempting to steal a march on Chelsea in pursuit of the player.
According to local newspaper Diario de Sevilla, Manchester United's negotiations with Sevilla were 'positive', and a transfer remains very much on the cards.