Mail Sport reported this week that PSG were in talks with United over a deal worth around £51million but those negotiations have reportedly collapsed.
Sancho improved his stock on loan at Borussia Dortmund in the second half of last season after being exiled by Erik ten Hag.
Yet despite the Dutchman insisting a 'line has been drawn' on their fracas, a new report claims their relationship is 'still strained'.
German outlet Fussball.news claims that Chelsea are willing to offer a transfer fee and two academy players as makeweights for Sancho.
Chelsea are reportedly prepared to table a bid for Manchester United star Jadon Sancho
Alternatively, the Blues would loan Sancho in with an obligation to buy, paying his £290,000-per-week salary in full for the duration of the loan.
Earlier this summer, Ten Hag suggested he and Sancho were on their way to repairing their fractured relationship.
'We spoke well. Anyone can make a mistake. If the player reflects well on that, then draw a line and continue again,' he told AD.
'This club needs good players, and one thing is for sure: Jadon Sancho is a terribly good player. I hope the click will come after all, and that it will contribute to our success.'
The 24-year-old was banished from United's first team last year when he hit out at manager Ten Hag after being criticised over his performances in training following a defeat against Arsenal.
Sancho at the time insisted he was being made a 'scapegoat' and subsequently refused to apologise to Ten Hag who decided there would be no way back for their relationship unless an apology was issued.
The pair have since made up and Sancho was an influential player in United's pre-season tour of the USA, also playing in the Community Shield final against Manchester City but missing his penalty.
Signing Sancho would see Chelsea's spending spree continue, with Todd Boehly's club having splashed around £160m on 10 players in another mad dash around the market.
Enzo Maresca now has 43 players in his squad and they have been trying to offload stars to ensure they avoid a potential PSR penalty.
Selling Ian Maatsen, Omari Hutchinson and Lewis Hall have seen the London outfit recoup around £86m.