Sancho joined Chelsea on the final day of the transfer window, with a deal sheet being submitted to the Premier League to sign him after the 11 p.m. deadline had passed.
The BBC reported Chelsea have an obligation to make the move permanent for a fee of 20 million-25 million pounds ($59.1 million).
Sancho joined United in 2021 from Borussia Dortmund on a five-year contract, but had a public falling-out with manager Erik ten Hag last year which led to him returning to Dortmund on loan in January this year until the end of the season.
He made a substitute appearance in United's penalty shootout defeat by Manchester City in the Community Shield earlier this month but was not included in Ten Hag's squad for their two opening league games.
Sancho made 83 appearances for United, scoring 12 goals and has played 23 times for England. He was one of the players who failed to convert a penalty in the Euro 2020 final shootout which England lost to Italy.
Chelsea host Crystal Palace in their next league game on Sunday.