The Daily Mirror's Darren Lewis claims the Brazil international didn't hold back on a challenge on Costa, described as “a particularly hefty tackle,” and the Spaniard replied in kind, resulting in a bust-up.
The two had to be separated but reportedly calmed down before heading for the dressing room together.
Oscar took to his Twitter account to deny the rumour:
For those who are talking to me and @diegocosta struggle today in training he's lying, he's one of my best friends and never fight 😉— Oscar (@oscar8) January 7, 2016
Costa and Oscar have been among the Blues' most disappointing players so far, although they have looked much improved since the appointment of interim manager Guus Hiddink.
Chelsea are unbeaten in their last four but still have plenty of work to do in the Premier League, where they sit just 14th in the standings, per WhoScored.com.
The Blues have to aim for silverware in other competitions, and per the report, the incident came during a "particularly intense" training session ahead of Sunday's FA Cup match against Scunthorpe United.
Fans likely won't be surprised to learn Costa was involved, as the Spain international has built quite the reputation for his physical style of play and aggressive demeanor since moving to England, per the Daily Telegraph.
Chelsea have endured a nightmare 2015-16 season so far, and these kind of altercations tend to happen when the atmosphere at a club isn't at its finest. The two will likely clear the air, and this incident should be forgotten before long.