Deal off: Mike Maignan
Chelsea Football Newsletter
But AC Milan are standing firm on their £25million valuation despite Maignan being set to enter the final 12 months of his contract at San Siro.
Chelsea had valued the 29-year-old at £10m but on Monday submitted an improved bid of £15m to tempt Milan's hand. Their offer was rebuffed.
It remains to be seen if Chelsea will go back to the negotiating table, with this transfer window shutting at 7pm tonight.
Chelsea begin their Club World Cup campaign on June 16, taking on LAFC in their opening group game, and need to have submitted a squad list to FIFA before that date.
If signed after the window reopens on June 16, Maignan would be ineligible to play for Chelsea at the Club World Cup until the knockout stage, before which the registration window reopens.
Transfer news LIVE: Double Arsenal deal; Chelsea make Maignan decision
Delap, Cunha and every major deal so far of summer transfer window
Abramovich outlines desire to one day make Chelsea return
Discover sustainable luxury at this breathtaking rainforest retreat