The European champions have held an interest in the France international for a number of weeks with Kurt Zouma being sold to help finance a deal.
However, Sevilla have since frustrated Chelsea by insisting that Kounde will not be allowed to leave for anything lower than his £68m release clause.
Despite reports of Chelsea being prepared to move closer to that fee, Monchi has hinted that a transfer now appears unlikely.
Speaking to reporters at a press conference, Monchi said: "The only written, formal offer from Chelsea came last Wednesday, around 5pm. We weren't satisfied with the offer, and it was linked to Chelsea selling a player. It was a decent fee but it didn't meet our criteria.
"We haven't spoken with Chelsea since Friday night. We all decided that it was best Jules didn't travel to Elche. It's normal for players to be affected by news of any kind. Last year he had the interest from [Manchester] City and now Chelsea this year.
"Kounde's clause never went up to €90m. It has always been €80m."
The 22-year-old is said to be keen to secure a transfer to Stamford Bridge before close of business on Tuesday.