The Portugal talent, who is the son of former footballer Sergio Conceição, is on the market.
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Per Record in Portugal, he is available for a £25million release clause, but only for a short time.
That clause will go up to around £38million next Monday, which means Chelsea are in a rush.
The Blues know they have to beat out other clubs and convince Conceição to sign in a matter of days.
Bayern Munich are one team that have cooled their interest, but Atletico Madrid and RB Leipzig are still in the mix.