The Blues have been in negotiations with the Serie A giants for the French stopper as they haggle over a transfer fee.
An opening offer of €15million (£12.6m) was rejected by Milan and it is believed that a deal could be struck for just €18m (£15m), meeting in the middle as the Italians value him at €25m (£21m).
In the grand scheme of football transfer fees it seems like a tiny hurdle to overcome, but a deal is proving more difficult than you might think
The report states that unless a transfer has been finalised by 7pm on Tuesday June 10 then Chelsea will walk away from a deal.
Chelsea offered one of Djordje Petrovic or Kepa Arrizabalaga to Milan in a proposed swap deal for Maignan, but the Rossoneri have no interest in either goalkeeper, favouring a cash-only agreement.
The 32-cap France international is out of contract at the San Siro in 2026 and could leave on a free transfer next summer.
The transfer window closing on Tuesday evening is unusual and has been brought in to allow clubs participating in the Club World Cup to bring in players before it starts.
There are now two transfer windows this summer, with the first running from June 1-10 before the Club World Cup starts on June 15.
There is then a second window which runs from June 16 till September 1.
The Sky Sports report states that the Maignan deal is different to the one that Chelsea are pursuing for Borussia Dortmund’s Jamie Gittens in that Tuesday’s deadline is not a final one
Discussions are ongoing over a move for the English winger and the Blues are happy to revisit them after the first transfer window closes if the transfer is not done in time
Dortmund turned down an initial bid worth €35m (£29.5m) for the 20-year-old and want a significantly bigger offer, closer to €50-60m (£42-50m
