The two are next set to meet when Chelsea travel to Old Trafford in the Premier League on February 25 however, the game may be rescheduled if Chelsea beat Bristol City in the Carabao Cup to reach the final.
"It was an accident, an incredible accident", Conte said on Friday.
Chelsea are, thus, keeping their options open, with a number of managers being on the shortlist to replace Conte, the latest being compatriot Allegri.
Appointed as Jose Mourinho's permanent replacement at Chelsea in 2016, Conte enjoyed a dream debut season in the Premier League as the Blues stormed to the title.
"I appreciate a lot this player because he is a really good player, Vardy".
Conte responded: "Before you make these kinds of comments you must pay great attention because you show you are a little man". This hint has come amid rumours the Blues are considering alternatives to the former Italy national team boss. "Conte's just doing what Mourinho used to do", the 71-year-old stated. "We all remember Mourinho on his knees in the middle of the field, running wild after his side won." .
The United boss infamously labeled Arsenal manager Arsene Wenger "a voyeur" when he was Chelsea manager and has exchanged a series of barbs with former Liverpool, Real Madrid and Inter Milan boss Rafael Benitez - and the Spaniard's wife.
The Italian's position has been the subject of speculation over a rumoured frustration regarding transfers.
"Football is this, our job is very hard as you know everything can change a few times".
Conte vowed to carry out an inquest into the problem on the training pitch.
Conte v Mourinho: Who said what?
"He is learning to deal with these type of situations, and if we speak about Batshuayi we are at the same level".
Leicester have lost 12 of their last 14 games against Chelsea in all competitions, and they are winless in their last 12 away Premier League games against "big six" opposition (W0 D3 L9) - losing each of the last five.
- Health officials warn of widespread flu cases
- New Poll: Majority of Americans Oppose Federal Intervention on Marijuana
- Turkey summons US Chargé d'Affaires over Syria issue
- Arab League Drafts Response To Trump's Jerusalem Decision
- Owner says Mike Mularkey is Titans coach for next year
- Judges angry about functioning of India's Supreme Court
- Fog warning for Flintshire - Thursday evening through to Friday
- President Trump reportedly refers to Haiti, African nations as s***hole countries
- Trump says he doesn't think Winfrey will run
- USA core inflation hits 11-month high