Diego Costa has been a revelation this season when firing home 10 Premier League goals, but Conte is not convinced with the rest of his attack and is looking to strengthen.
Muriel himself is in good form when firing home eight goals in 15 appearances this season, and his form has caught the eye of Conte, who could now launch a bid.
Reports in the Italian press have suggested that Sampdoria would sell for a fee in the region of €28million, and the Blues would have no problem matching it.
Any move for Muriel would cast further doubt over the future of Michy Batshuayi, who only joined Chelsea in the summer for £33million, but has struggled to impress.
AC Milan are keen to do a deal, as are West Ham, and Conte would be happy to cash in and use the cash to sign Muriel.