Manchester City have reportedly made a formal complaint to referees chief Mike Riley over the officiating performance of Michael Oliver during their defeat by Liverpool at Anfield on Sunday.

Oliver and VAR were at the centre of a refereeing storm after City were denied two penalty claims for handball against Trent Alexander-Arnold, with the first incident leading to the hosts' opener through Fabinho.

After the second incident, City boss Pep Guardiola fumed at fourth official Mike Dean over the decisions, and at full time he said to Oliver: 'Thank you, thank you so much.'

Man City have made a formal complaint over the refereeing performance of Michael Oliver

At full time City manager Pep Guardiola said to Oliver: 'Thank you, thank you so much'

City have since sent a letter to PGMOL chief Riley on Monday, just 24 hours after the crunch clash in Liverpool.

The Premier League champions remain baffled as to why Oliver did not award them penalties for the two incidents, while Guardiola and Liverpool boss Jurgen Klopp aired their qualms with the use of VAR at the UEFA summit in Nyon earlier this week.

According to The Sun, Riley is said to have responded 'constructively' to the letter ahead of a shareholder meeting of all 20 Premier League clubs set to take place on Thursday, in which the chief will give an update on the implementation of VAR.

City were denied two penalties for handball in their 3-1 loss to Liverpool on Sunday

When asked whether he felt decisions had gone against his team, Guardiola said on Sunday: 'Which decisions? Oh. Mike Riley and his people – you have to ask them. It would not be nice after we lose to (complain). Ask Mike Riley and the big bosses about it.

'I said thank you every much. I said the same in the Tottenham game at home (when City were denied a last minute winner by VAR). Thank you so much. Most of the time when I go to the referees and my colleagues, I say thank you so much and good luck.'

When it was put to him that Riley does not make himself available for interviews, the City manager said: ‘That’s the point. You talk about the game. I am not hear to talk about the referees. Ask to them, my friend.

PGMOL chief Mike Riley will stand before the 20 Premier League clubs on Thursday to explain his thoughts on how VAR is being used this season

‘All the time I have to come here, to speak about the decisions and the VAR and the referees. Why? One day it is a hand. The next day it is not a hand. Don’t ask me, ask them. Knock on the door. Phone call. Maybe they can answer. But don’t ask me. Please.’

It is unlikely that any wholesale changes to the use of the technology will be brought forward on Thursday, unless Premier League clubs dramatically revolt against VAR.

Riley will explain to the clubs that VAR has been a success so far this season, with one in 10 key decisions being decided incorrectly, a huge improvement on the one in five figure last season.

The letter comes after Neil Swarbrick, the man who was responsible for introducing VAR technology to the Premier League, said he was happy with how it is being used.

Bernardo Silva opted not to speak so as to avoid punishment from the Football Association

'I'd give us around about seven-ish,' he said. 'If the mark now is seven — early days — in two years' time I'm hoping for maybe a eight and a half or nine. We are open to evolving with this.

'It's not a case of we're not budging. We will listen to feedback. I'm comfortable with where we are but there's no doubt there's room for improvement. It's a work in progress.'

It wasn't only Guardiola who was dismayed with the decisions of Oliver during the game at Anfield. City attacker Bernardo Silva channelled his countryman Jose Mourinho in refusing to be drawn into questions regarding refereeing decisions.

He said: 'If I speak, I will be in trouble. I don't want to speak.'

The aftermath of Sunday's game have spilled over into the England camp, too, with City's Raheem Sterling and Liverpool defender Joe Gomez involved in a bust-up at St George's Park on Monday.