Kondogbia has impressed since signing from Lens at the start of last season and has been linked with a move away this summer.
Premier League quartet Manchester United, Manchester City, Chelsea and Arsenal, as well as La Liga giants Real Madrid and Ligue 1 side Monaco, are believed to be tracking the midfielder, who made his full France debut against Belgium earlier this month.
Sevilla have already sold Alvaro Negredo, Jesus Navas and Gary Medel to Premier League clubs for big money this summer and so are not under any financial pressure to sell any more star players.
They have made it clear they will resist any bids for the 20-year-old, though a reported €20million (£17.2m) release clause in his contract means they would be powerless to stop the player from talking to clubs who meet that fee.
Speaking after their 3-1 home defeat to Atletico Madrid in their La Liga opener on Sunday, Emery insisted the club are desperate to keep Kondogbia at the Ramon Sanchez Pizjuan.
"We want to have continuity at Sevilla. I have spoken with the president [about Kondogbia] and only a big-money offer changes that idea," he said.