The Football Association is aware of the controversy at the match and is waiting for Oliver's report.
Oliver will be asked by the FA whether he or any of the officials saw the incident and if they did not, then to judge from video replays whether either of the incidents were straight red-card offences.
If the referee believes either was a red-card offence then the Spain international will be charged with violent conduct and dealt with under the fast-track system
It would mean that if he is found guilty any three-match ban would see Costa miss Chelsea's game against title rivals Manchester City at the weekend and the matches against Everton and Aston Villa - and there is no right of appeal
It is understood, however, that it is unlikely he will face two violent conduct charges.
As the Capital One Cup is a Football League competition, the disciplinary process differs slightly from a Premier League match where a three-man panel of former referees would decide whether he should be charged.
Costa was accused by Liverpool of stamping on Emre Can at Stamford Bridge and then a further stamp on Martin Skrtel.
Chelsea manager Jose Mourinho has insisted that both stamps were "absolutely accidental".
Source : PA