The Bayern Munich star has struggled to make an impression on the Bundesliga side since his big-money move from Benfica.
United boss Jose Mourinho is a long-term admirer of the 19-year-old and reports claimed last week the Red Devils were considering a bid.
And the Blues are thought to have joined the race after the youngster’s impressive display against them in their 3-2 defeat to the German giants on Tuesday.
The Mirror claim Antonio Conte asked Bayern about £30m-rated Sanches following the match.
The Telegraph claim Conte is interested in taking the £30 million Portuguese star on loan for the season and has made an enquiry during Chelsea’s pre-season tour of Singapore.
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