The Star on Sunday reports that the Blues will make a £20million bid for the 24-year-old in January.
Chelsea are desperate to beat Tottenham to the signature of the former Celtic midfielder.
Wanyama joined Southampton in a £12.5million deal from the Scottish giants in 2013.
Tottenham had a £18million plus Erik Lamela on loan bid in the last days of the transfer window rejected by the Saints.
