Manchester United were undone by a late Diego Costa equaliser at Stamford Bridge, which set them further back in their race for the top four.
The Red Devils were held to a 1-1 draw and are now six points off fourth place, with an inferior goal difference to all four teams above them.
Missing out on Champions League football for a second time in three seasons is a genuine possibility, and this could put the future of their stars in doubt.
One player about who there will be continued speculation is David de Gea, who was silent on his future all last summer and almost move to Real Madrid.
BBC pundit Garth Crooks, who selected the Spaniard in his team of the week for his display against Chelsea, believes appointing Jose Mourinho as manager in place of Louis van Gaal is United's best bet to keep De Gea.
He wrote in his BBC column: "If United were to qualify for the next season's Champions League it would help matters enormously but if they fail to make the top four then that would almost certainly lead to the departure of the Spaniard - as long as Real are allowed to buy players.
"However there is one last scenario - Jose Mourinho replacing Van Gaal as manager might refocus his mind."
Mourinho is the bookies favourite to be the next United manager, even though Van Gaal dismissed this as 'nonsense', reported SkySports.