It seems that the negative attitude at Chelsea has spilled over into training ground anger as reports emerged on Thursday evening from Cobham that clashing teammates had to be separated earlier that day.
Brazil-born Spain striker Costa took exception to a challenge from Brazil playmaker Oscar and responded in kind in a competitive training session, with a confrontation swiftly diffused.
Team-mates and coaching staff reportedly stepped in to calm the situation down. Once more, the pair were separated.
No punches were thrown and both players were seen laughing as they walked off the training pitch.
Blues interim manager Guus Hiddink may be asked about the alleged standpoint in his news conference on Friday.
"Those who are saying that Diego Costa and I had a fight in training today are lying, he is one of my best friends and we would never fight", Oscar tweeted.
Falcao was hoping to resurrect his ailing career at Chelsea this year, but halfway through a season-long loan with the Premier League champions, he has scored just one goal.
However, Mourinho's departure has coincided with a return to form, with Costa having scored three goals in Chelsea's last two matches.